Do the BSA Martini .22s seem to have a decided preference one way or the other?

Probably depends more on the model and factory or custom forearms. Mk-3 have a free float forearm as opposed to the rest being fastened to the barrel. Most factory forearms are designed for position shooting so don’t have wider flatter bottoms to enhance bag riding. 
Barrel sleds can be a big improvement on most. JMO

I use a sled on mine, the previous owner rested it on the forend. I found more consistency on the sled

Probably have him start with the normal things; hold steady, squeeze gently and try at least 10 brands of ammo (put at least 20 rounds of each one through the barrel before shooting for group).
Once he gets a good match for the rifle then he can tweak it by searching for the sweet spot on the barrel for a rest. Start about 2 inches from the muzzle and shoot a group then repeat at three inches, then repeat at 4 inches, then 5 then 6. If one shows best then bracket it by a half inch either way. Pick the best, mark it with a small piece of tape and go with it for a while.

I’m not really sold on sleds. You don’t see ARA folks or NBRSA folks use them. In fact I’ve never seen anybody win a match with one in person. 
IMHO I think a windage adjustable front rest, a solid bottom rear bag, wind flags and good ammunition could take your friend far. 🙂