I'd consider sleeving the chamber and the throat. Done as far in as the chambering reamer will cut a new throat for you so the new chamber and throat flows nicely into the old bore. You get a new chamber and as much of a new throat as possible to get rid of the old burned up one.
Done right and with a tight metal to metal fit joint up front, it'll stand up just fine with any 30-30 loads I'd want to put thru a skimpy bbl'd drilling of that age.
Sleeving just the chamber or the chamber and throat of the bbl was not an uncommon repair on single and double rifles in low pressure rounds.
Some were done better than others of course.
You could even do the new chambering in 32-40WCF w/a 30cal pilot on the reamer. Then size the 32-40 brass FL but do not expand them. They then hold .308d bullets just fine.
32-40 pressures are quite a bit lower than 30-30 IIRC.
JMO and thoughts
It's hard to be dogmatic without seeing what those thicknesses actually are, but my guess is that this would be the best way to go. Of course you would have to reduce the wall thickness, just as you would with the .30-40, but you would be filling that space with a metal sleeve, so lose-fitting that if the pressure did expand it beyond its elastic limit, it would impose no further risk. This is rather like the principle known as autofrettage in artillery, in which stressing of the inner layers can actually strengthen a barrel.
The thin walled aviation stainless tubes are well worth looking into, for they are extremely tough. There was a vogue in the UK a while back for using them to line shotgun tubes, although this declined due to the effects of extreme heating, and the difficulty of dealing with a dent. You would have to use something like the bearing-fitting grades of Loctite, since the barrels and ribs are presumably soft-soldered.
.22 WCF, .22 Savage High-power and .25-35 were all fairly popular in Europe, and gained their own metric names. I don't believe this was the case with the .30-30, which is unusual to find in a gun of this type. My guess is that it was rechambered from one of the multitude of mostly forgotten 8mm. or 8.15mm. straight-tapered combination gun cartridges. These often had a thicker neck than the .30-30, and almost all used the groove diameter of the J-bore Mausers. This is usually listed as .318in., but could easily have been on the tight side. It would let you in for using something like Bertram brass, but the straight taper would put more strength into the sleeve and barrel, and one of the longer ones would eliminate much of the throat erosion.
