These regular Model 70 classic stocks are, to say the least, boxy. The super grade ones are nicely rounded.

I'd like to try my hand at making a boxy one round.

Any suggestions (besides "don't do it because you'll screw it up).

I've read that the way to do it is to strart rasping flat surfaces and then rasping the corners to make even smaller flat surfaces and so on and so forth.

If you go to youtube.com and type in Midway USA you will get a lot of short videos on this subject. Larry Potterfield, owner of Midway, does what you talk about, filing flats and then rounding them. A bit of advice...he makes it look a lot easier than it is as you can easily remove too much wood real quick. My suggestion is to find some old stocks and practice before you work on your M70 stock.
I agree with you on the shape..I have an early post 64 in 458 that has the original supergrade shape, and an original supergrade 300 H&H. Those two are much nicer feeling stocks, IMO, than are any other Wincehster M70 stock.
The bad thing about the videos is that they are usually less than 2-3 minutes in length, so a lot is skipped. I watched the one on glass bedding a rifle, lasted about 1.5 minutes...don't think it is really that easy!