Postoak already mentioned the 30-30 A/I,,,,
I believe a rechambering to 30-30 Ackley Improved (30-30 AI) would solve the most severe problem you have of the erosion ring at the bottom of the case shoulder in the chamber.
That's not allowing you to even fire the rifle bbl w/o pounding out the empties from the muzzle.

Here's a link to another unrelated forum and discussion but there is a side by side pic of the standard 30-30 and the 30-30 A/I chamber dimensions. Scroll down the page on the link.

Quite helpful I think in figuring out if the latter would clean up the problem existing in the chamber now..
https://www.24hourcampfire.com/ubbthread...nd_cast_bullets

The 30-30 AI expands the case body diameter behind the shoulder and moves the shoulder forward (resulting in a shorter neck).
That larger dia case body reaching farther forward may remove that erosion ring causeing the extraction problem.

It'd still chamber and fire standard 30-30WCF. The cases would just fireform to A/I cases.
Minimum material removed from the bbl, no rebore, relineing, ect.

Keep loads (very) reasonable and I think the gun will never know the difference and could be usefull once again.

As for the throat erosion,,perhaps it isn't as big a deal to shooting quality as you might think. Try it w/o any changes. Then if you think cleaning it up a tiny amt by extending the throat and loading the bullets out further will help,,it's a simple hand reamer job.

Chamber reamer rental is quite reasonable these days from a few sources. The 30-30 A/I is generally a common stocked item.
..as are 30cal throating reamers.

,,,,,
The only other thing I can come up with is to run a 303British reamer into the chamber and push the shoulder forward. That'll recut the neck slightly larger than it is right now of course. But you seem to have 'an oversize neck' problem too..
Run the reamer on a .308 pilot of course.

Only deepen with the 303Brit chambering reamer to the depth that the taper of the body of the 303 reamer meets and matches the base dia of the 30-30 chamber (.422d).
The shoulder of the 303Brit chamber and the shoulder of the 30-30WCF chamber are the same at .401d.
Even the shoulder angle is within 1/2 degree.
So perhaps the 303reamer being tapered more than the 30-30 as it cuts deeper, pushing the shoulder forward AND will clean up that erosion ring problem.

You will of course end up with a wildcat sort of a short 303Brit w/a 30-30 case head size.
Depending on how deep this crazy idea allows you to go before the 303 reamer starts to cut away the 30-30 chamber base,,perhaps you can still use 30-30 brass,,or maybe 38-55 brass (a little longer I think.
Size in a 303Brit die and load. Don't use an expander,,just size the brass and 308 bullets will seat just fine.
Or .311 lead down a .308 bore won't hurt with light loads.
This should cut a nice new clean throat in the bbl for you too.
All 3 problems taken care of..!

....if it works of course..Just a goofy idea that's all.