To what extent is being a quick problem solver (e.g. doing well in brain teasers) predictive of research success?
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 &quot;maxed out&quot; 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 :)