204Ruger

What is the recommended torque spec for the take down screw on a 10/22 with the barrel floated?

Both my 10-22's are custom, both bedded with Accuraglas. I also use a hex takedown screw and tighten it down using the Allen wrench just past "snug". Completely subjective and meaningless, but that's all I can offer, as I don't own one of those neat little Wheeler adjustable torque wrenches. Without one, just plain old common sense comes into play here. You want tight, but not too tight to compress the wood.

One thing I'll mention, is that with the heavy breach block/bolt in these rifles, the takedown screw can come loose from extended firing.....ask me how I know. To solve this, I put a tiny dab of blue Loctite on the screw to keep it in place during a good, robust rat shoot, usually firing out the truck window off a window bag during less than stellar rat shooting weather when bench shooting ain't happening. Since doing so, no more takedown screws backing out.

P.S. Another thing these rifles benefit from is the use of recoil/shock buffer for that heavy breach block hammering back and forth. Power Custom, Volq, etc.

Depends on how free floated your barrel is but...
What I have found with wood stocks, snug them ‘over tight’ until the groups string vertical. (Thanks to the Ruger barrel droop syndrome) Then back it off in very slight increments and you’ll see the string slump into a group. Past the sweet spot it will open back up. Tried numerous values 18-24 inlbs with torque wrenches, certified or Wheeler made no difference. Each was slightly different. Synthetic stocks seem to like it tight and there is less need to dither over torque. Kind of a crank it down and shoot.
And I second it on the bolt buffer and locktite.
There is no end to the mods.