No doubt the 700 footprint makes stocks easier, but barrels are available for the 77/22. A qwik search showed barrels from Shilen, McGowen, Lilja, and Clark Custom (Walther blanks) along with the more commercial players like TacSol. Maybe they're not the high-end of stocks, but if wood is the go-to then Boyd's shows many solid options for a stock. Same for triggers, Timney, Rifle Basix, and MCarbo were all found qwikly and there may be other options.
Frankly, I'm not sure that I'd want a 700 footprint based .22LR action. Just seems grotesquely larger than necessary. That's not to suggest that my next build will be an M77/22, but it might be!