Of course you _can_ set the action just as low on a strat, it just won't work well for bends simply due to 7" something radius fretboards on classic strats...that's why you will never be able to get _quite_ as crazy low an action as on a fretboard with like 20" radius or so....but well low enough anyway...still, it's no bull and a big reason for having super flat fretboards is indeed getting the action crazy low.

For shimming, don't bother with wood shims, you will find you actually need VERY little shim there to change the angle quite significantly, wood is almost certainly overkill.

At some point, strats used to come with 3 screws where the 3rd one adjusted the angle; having the neck sit in the pocket supported by one metal bit didn't however entirely ruin the sound even on those, so never mind about perfect contact there...I've seen for instance metal spacers placed in the pocket and that works OK as well.

What I'd recommend is use sanding paper; any grit, but try some rather coarse like 80 maybe. Cut 2 bits of sanding paper, one that's like half the size and one that's 1/3rd of the size and lay them in the pocket to form 'stairs' ascending towards the body so that the paper sides face each other. Or, might be just one slice of sanding paper will be enough, positioned near the back of the neck...or even three but I doubt it.

Sanding paper is thick, will stay securely in place and 'bite' into the wood well yet the grain allows for some compression and it becomes quite flat and filling when the neck is screwed in place. Try it first. Learned this from a luthier who much rather uses sanding paper than wood shims.