Look up the Lazzeroni, big Wby, and Gibbs based monster cases. NONE provide a substantial increase in performance VS the huge amount of powder burnt when comparing small cals.
Overbore is lots of fun and I have been there and built the rigs. You quickly see that a quantum increase in powder yields very little extra velocity unless you go to super long barrels.
The powder options plummet and wet sawdust starts to look promising. Maybe crushed briquets.
Then you get bullet blow ups due to friction while zinging down those bores AND the jackets distorting due to super high rates of spin AND pressure.
The 90gr VLD's ingeneral have thin jackets (you might get the Berger 90gr BT and Sierra 90gr MK's to sing though) so will not tolerate being pushed that hard. If the bullets make it, accuracy is rarely good.
About the only bullets that seem to tolerate this abuse are the MK's and Hrn Amax. I have heard some shooters pushing the 80gr Amax over 3600fps with decent accuracy
There are several boards with data on this super big case 22's. They have all been done before. 1970's was when they last saw popularity. Middlestead, Cheetah, Jaybird, Swift improved, 22WSSM are just some of the options.
I have an old article on a 22-284 so you aren't even into the silly big.
You have a middlestead so you are set up to go. You also have a 22.250ai that just needs a new pipe.
You already have plenty of experience with these zappers. A 22-308 is really not much different.
I spent years wildcatting so don't let me stop you build the next toy. But I don't think you will see the performance you are expecting and the bullets may just let you down.
Jerry