Dakota 76 issues

Sounds like maybe the spring under the follower is in backwards.

Chad @LRI might have some insight.

The problem is going from 22-250 to 6.5 CM. Many mags and box mags will not handle both equally.
The 6.5 CM is much wider at the shoulder and larger longer bullets and cartridge overall length much longer.

Internal bullet and cartridge guides can be much different between these two.

Easy button is simple, put the barreled action in an aluminum chassis made for this action, ...bolt it down.
And buy 6.5 CM mags/ 308 mags ...center feed get longer COAL for extra performance, and usually accuracy, by getting bullets close to the rifling.

If the stock is one you really like it can be inletted for different bottom metal that takes detachable mags.

Your choice.