For purposes of the ATF I've got a couple recommendations.
1) Use a virgin aftermarket action.
You're spending the money on a nice barrel, stock, trigger, and so on. Why stick to a stock action?
2) Find a Ruger Charger, the pistol version of the 10/22, to base your build on.
I'd start with a pistol. Either by buying a Ruger Charger, or build a virgin receiver into a pistol before doing your rifle build. Reason I suggest this is because you are allowed to convert a pistol into a rifle and and then revert it back into a pistol as much as you like. Document it with photos that it was first built as a pistol. Then build your rifle. Doing it this way, you can legally swap the stock back and fourth and shoot pistol or rifle comp if you want. The only thing to watch out for when doing this is to never have a <16" barrel installed with the rifle stock installed, unless you Form 1 SBR the receiver.
IE:
Purchase a Charger, install a 16"+ barrel first, then install a rifle stock, and you've got a perfectly legal 10/22. When you are ready to use it as a pistol again, reinstall the pistol stock first, then install barrel in length of your choice, and you've got a perfectly legal Charger.
Purchase a 10/22 rifle, and install a <16" barrel and you've got a SBR. Install a Pistol grip and the OAL is less than 26" and end up with an AOW. Both of which are NFA firearms and illegal unless registered. If you install a pistol grip and a short barrel it's still a SBR due to minimum barrel length requirements.
If you decide to go the aftermarket route and also take my pistol suggestion, apparently you can not use KIDD receivers because they register them with the ATF as rifles before selling them. Most virgin stripped receivers are considered as "Other" on the transfer forms.