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I hope to begin a PhD in the near future in a technical field. I feel that my strength is in being able to ask interesting questions / come up with a creative high level approach / make new connections between fields or ideas (several of my mentors have commented on this) and being extremely motivated and hardworking. I've done pretty well as an undergrad and one of my mentors told me that I shouldn't have trouble getting into my top choice PhD program.
However, my huge weakness is in quick thinking. I am embarrassingly slow to answer "brain teaser" type questions and feel that essentially all of the people I interact with in a research context are way faster than I am in their speed of problem solving and understanding technical papers.
So my question is: for those of you working in fields such as computer science, statistics, applied math - how important is raw speed of technical problem solving? Can I compensate for my slowness with hard work, or will I eventually reach some ceiling? I sometimes consider switching to an "easier" field, but I don't like the idea of giving up ...

It has taken me some time to see myself clearly (in large part because I had perfect scores on almost all standardized tests back in high school, and so thought I was "smart" ...), and after frankly looking at my strengths and weaknesses I suspect I might do better in a field where asking the right question is the most important part, and answering it is largely a matter of being motivated and conscientious. However, I can't think of any such field that truly excites me at the moment, and that also has reasonable exit options outside of academia.

I hope to begin a PhD

understanding technical papers

You should not expect to understand technical papers even as an advanced undergraduate. These are often written to impress and placate referees more than to make readers' life easy. Sure, some papers will be fun to read, but most of the time reading a paper is a painful exercise in balancing between patience and criticism. I have read 0 non-expository papers in my 5 years of undergrad.

how important is raw speed of technical problem solving?

As a cause: probably fairly unimportant. Your output won't suffer much because you are a slow thinker. Researchers don't usually spend much of their time solving problems; it's closer to 10% problem solving and 90% bookkeeping, teaching, and other chores. If the former 10% take up 20% of your research time instead, well, you'll have a little bit less spare time then, or do worse at teaching, or compensate otherwise.

As a symptom or correlate: possibly, if the theories about thinking speed being (highly correlated to) a central component of intelligence (read the unending flamewars around Spearman's g if you think modern science has gotten boring) are true. But if several of your mentors have vouched for your motivation, willpower and creativity, you're likely not in much trouble either way. Very few scientists have "maxed out" all these attributes together.

Sorry, this was somewhat of a reddit-style answer, but then again it is a reddit-style question. Quantitative results are scarce. I don't recall seeing any studies correlating academic success with thinking speed; most studies use measures like SAT, which themselves are mediated by thinking speed. Feel free to respond with citations :)

I've done pretty well as an undergrad and one of my mentors told me that I shouldn't have trouble getting into my top choice PhD program.

I think there’s your answer right there, staring you (sort of) in the face. You will apply to grad programs, and the best and most experienced researchers out there will take all the data you and other applicants will submit, and use their best judgment to determine who among this group has the highest potential to succeed. If you get admitted to a top program (a big if - it’s certainly nice that your mentor says so, but I wouldn’t pop the champagne just yet), what that would mean is precisely that to the best of anyone’s ability to predict based on available data (which is much more data than is available to us here on this modest forum), you would be as well-positioned as anyone else to succeed in research.

Put differently: if grad programs thought that being good at quickly solving brain teasers was important, guess what - they would very likely try to have you solve brain teasers as part of the admissions process. Since they don’t, well, that kind of tells you everything you need to know about whether that’s considered an important skill...

By the way, everything I said above also applies if you get in to a very good program that happens not to be at the very top of your list. Plenty of really smart people end up in those programs. So basically, the admissions process is precisely the kind of evaluation that has been optimized over many years to measure (as best anyone is able to do that) your potential to succeed. There is no need for you to come up with other, external metrics. Just give it a shot, and if you get in, that by definition means you’re qualified. Good luck!

Answer after edit:

If you are getting perfect scores on standardized tests, I wouldn't doubt the general horsepower. Perhaps there is some very specific aspect of mental processing that enables you to perform well on GMA tests, but not on brain teasers. And perhaps even there are fields that benefit from fast brain tease ability. But this is a subtlety, among many when you look at what to do with your life (which has no Euclidean answer).

However, the comment on picking right problem is very interesting. One of the most important aspects (very underrated) is having good intuitions about which problems are high likelihood of success. Lot of sad stories from grad students who spin their wheel on "a problem the boss gave me". Conversely I picked something I knew would work, sounded cool, and was cool; and project selection made my time so much more calm. I think almost every field has cool problems and that when you get into it you will find them, especially if you think identifying good problems is a skill of yours. Specifics will come from getting into the field though.

Personally I would go towards whatever interests you. One small advice I would give is not to underestimate the experimental or applied sciences. I was the classic "math science" type who wasn't perfect at a lab notebook and test tube cleanliness (and was scared by subjects involving difficult experiments or apparatus building...figured I was a pencil/paper type). However, the truth is that a lot of what determines success in those fields at the real research level (as opposed to school courses) is picking projects and ability to read and interpret the literature. And they are a lot of fun...

Answer prior to question edit:

Your question is rational and candid. We all have to look for comparative advantage.

There is a huge literature showing a correlation between IQ and performance in mentally complex jobs. See, for example, meta studies by Hunter and Schmidt.* (It is the strongest statistical relationship in nonpathological psychology.)

Of course, nothing is 100% as a predictor, but in general there is a certain amount of smarts needed to handle some areas like grad physics (Jackson E&M) and grad math (God knows). And having more seems to be better even for those who have the minimum in those topics.

Again, it is not a 100% predictor. Neither is speed or strength or size for certain sports. But it is a strong factor. Consider that there have been only 25 NBA players in the history of the league who were 5-9 or less. Conversely if you meet a 7 foot man, there is a 1/6th chance he has or will play in the league. So obviously specific traits (talents) can influence performance at high levels.

Note that there is some sorting of and probably different floors by academic topic. With the more mathematical topics needing more horsepower and the more applied ones less. See XKCD: https://xkcd.com/435/ However, be of good cheer. The good part is the more applied ones are more interesting--more hair on the ball, more direct connection to industry/society. Or so I tell myself to feel better for not solving Fermat's Last Thereom. ;-)

*Link: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.172.1733&rep=rep1&type=pdf I think this is the classic summary paper of theirs, but they have published several others, including some more recent.