All of the other prep I've used suggests reading the question first. Why us this not a good idea? I feel like switching strategies this late might be harmful but it might be worth trying.

Joseph,
The answer is a little unsatisfying: you should use whichever approach works best for you.

The advantage to reading the question stem first is that you will know HOW to approach the passage before you start reading it. So if you know you're answering a "main point" question, you'll know before you start reading that you have to isolate the conclusion. If you know you're answering a "flawed reasoning" question, you know you've got to read the passage with an eye toward finding the flaw.
The downside to reading the question stem first is that the passage may be constructed differently than you're expecting. This can make misreading errors more likely, because you'll be rushing through the passage trying to find the conclusion/error/etc.

Reading the passage first allows you to get an unbiased picture of the argument, and to evaluate the argument on it's own terms. This is really good for obvious reasons, and one of our contributors (Nathan Fox, an LSAT instructor who has over 5 years experience and who scored a 179) is a strong advocate of the "passage first" approach.
The downside to "passage first" is that you may have to re-read some passages after reading the question stem. This can be a time suck. Also, you're more likely to be rushing once you get to the question stem, so you're more likely to misread it.

Regarding a late (2 or 3 weeks before the test) switch, I'd say this: try the "passage first" method on two complete LR sections. Check your scores against your average. If your new scores are more than a few points below your average, the learning curve will probably be too steep for you to switch now. If you're close to your old averages, try the new method for 2 or 3 days. See how it feels, and switch back if need be.

If you've got less than a week to go, don't switch.

Biggest thing to remember: "passage first" or "question stem first", the goal is the same. If you understand the underlying principles, you'll be fine.

Thank you for the always awesome advice.