According to an old grammar book I have (and also in Bartleby on line)-
Might I express my opinion conveys less insistence than May I express my opinion.

I dunno. I have heard people in heated argument use both MIGHT I EXPRESS...., and MAY I SAY....; both very insistant about their viewpoint.

(Years ago I went out the back door of a used book shop to get to parking, and saw a trash barrel full of books. Some were on English usage and grammar, and I took a few. I still have one or two, but I followed the book dealer's example with most of them.)