Seems like the only two options are clamping it directly to the barrel (which could potentially affect accuracy) or drilling into the fore end to add a stud (which I would rather avoid).

Are there other solutions I’m overlooking?

Edit: The Magpul backpacker stock not the hunter.

I have tried a bipod and a scope mounted on the receiver.

Too much flex.  No matter how tight the barrel lockup... you won't be able to shoot a decent group.

Are you using the factory barrel? I’m wondering if something like a TacSol barrel will be heavy enough to mitigate the flex.

I have one with the factory barrel and one Tacsol barrel.

Same problem.

The problem with the takedown 10/22s is that no matter how tight you get it to lock up it will never be as stable as the regular versions.  This becmes very apparent when shooting from a bench or with a bipod.  For general plinking/hunting though it works fine.

I do have a take down, but I haven't shot it yet,
so I can't speak to that part of the OP's question.

All of my 10/22's have polymer stocks & I have
added short magpul pic rails to the bottom front
of the forearms & I have a couple of pic rail bipods.

I can easily install bipods whenever I need them,
and remove them for transport, etc, and they are
not dedicate to each rifle.

I also added the pic rails to all of my AR's for the
same thing.

Cheap, easy & effective.

I don't remember what brand mine are but here
is an example.

Primary Arms

If you take-down the 10/22TD you'll quickly notice how little meat the barrel extension has on it, and the whole barrel is levered out past that. There is a hard 90* cut that probably doesn't help with barrel harmonics. I'd bet the heavier contours perform WORSE under bipod loading.

When I shoot mine I set the gun up so it's resting on bags right at the joint between the two halves and I don't bear down on the rifle. If you lean into the gun you can create a repeatable POI shift.

I still like my TD but it's not the tack driver I wanted it to be, more like a fun plinker. Looking at the RAR-LRT or a CZ to scratch that itch