I had to pull my M77 out of the safe to look it over before posting.
I assume your intention to free-float the barrel is to improve grouping ability. If I were to free float, here's how I would do it...
Free float by only removing wood from the barrel channel in the stock.
The action sits on a flat shelf within the stock and putting plastic shims under the front would make the action sit cockeyed and put unusual stresses into the receiver (bad for accuracy). When installing the receiver in the stock, check to make sure the magazine box isn't hard bound up between the receiver and floorplate. If it is binding, shim the floorplate and trigger guard out from the stock with some thin cardboard shims cut to shape. The idea is the mag box should not put stress on the receiver. I also check to make sure there is a slight gap between the wood and receiver tang running forward about 3/4 inch from the tip of the tang. That gap also prevents a nasty crack from developing in the wood as the rifle is shot many times.
Snug (not tighten) the forward screw first as it sets at an angle to pull the action tight against a recoil shoulder in the stock. Next snug the middle screw then the rear screw. Then go back to the front screw and tighten it. The front screw should be the tightest of the 3 screws. Then tighten the rear screw. Leave the middle screw snug (don't tighten).
You'll know if the barrel is free-floated if you can slip a dollar bill, folded in half lengthwise, between the barrel and stock from the stock tip back to the receiver.
I haven't had to mess with the bedding at all, so far. 1/2-MOA for three shots, with most any old ammo. I did put a Timney trigger in it.