Interesting feedback. My TR rifle's barrel is not what it used to be, and the rifle is basically a converted Palma rifle anyhow. I thought I'd use it for sling shooting until the barrel just quits, but it's got a long (.200") throat. Sounds like I ought to give a few bullets a try. I'm not expecting miracles (it's a 10 twist, long-throated, half shot out barrel, after all), but if I can get them to shoot even moderately well, I'll be satisfied until I get a new barrel. I'm not a terribly good sling shooter.
You may be surprised just how well some bullets shoot, but you need to do your load development with a chronograph as MVs will be seriously down for any given powder charge and a significant increase will most likely be needed. (As Monte M says above in post #6.)
I'll quote two personal examples akin to yours. My first 'proper' TR rifle was a first generation Schulz & Larsen Mauser '98 based job that had had 20 or so seasons of factory 7.62 ammo through it. Due to throat erosion, freebore was massive - you couldn't get a bullet anywhere near the lands. So I loaded up the longest bullet commonly (and cheaply) available to us at the time, Lapua's D46 185gn rebated-boattail FMJBT barely in the neck and worked up a charge of Hodgdon BL-C(2) that was some 5gn above book maximum. It shot very well for a season and a half until the barrel failed dramatically mid match one day and 1-MOA precision became 4-plus. We didn't have chronographs then, so I've no idea of MVs as a result of the freebore.
Then, more recently I acquired a Paramount TR (sling shooting) rifle sans iron sights as an 'affordable FTR' project to be rebarrelled with a Heavy Palma profile 10-twist barrel. The project never happened for various reasons and I took to plinking with the rifle as was once I managed to get Evo Leisure (the Tier-One people) to design and make a scope rail. The rifle had a 30 or 31-inch Light Palma Lothar-Walther 1:14 twist barrel on it with very 'tight' internal dimensions. Both twist and dimensions point to it having been put on when 144-146gn Milspec 7.62mm NATO ammo was the norm in UK TR shooting, ie many years before and knowing of the previous owner, I know the rifle had been in use for a long, long time with likely a massive round count. (When I asked him direct, he was evasive on the issue, but mutual friends told me how many years this barrel had been in constant use.) As with the Schulz & Larsen, there was massive erosion, but as was common with these rifles used with lower pressure military ammo (especially with the notoriously 'tough' steel in L-W barrels) the eroded throat was smooth and there was no firecracking ahead of it. The then standard GB NRA TR 308 ammo - RWS loaded with the 155gn SMK #2155 to a nominal 2,925 fps in a standard spec TR rifle in good condition would average sub 0.5-MOA 5-round groups off the bench at 100, the best being a single hole (!!) but MVs were WAY down - ~200 fps IIRC.
I shot lots of mild 168gn SMK handloads out of it in this form and it did fine at short ranges despite the 1:14 twist being marginal. The 'trick' with barrels in this condition is to choose very jump tolerant bullets like the old model 155 SMK and 168, 155.5gn Berger etc. I did try the 155 Scenar and it was 'rubbish' - that may well have been the 14-twist, but I suspect also the Scenar's fairly marked secant ogive, even if it isn't a full-house VLD form was a factor. I never measured what the SMKs were jumping, but it had to be well over 100 thou', more likely 200!
(The rifle is still my 'old man's low-cost short-distance range plinker'. It has a recycled 10-twist Krieger on it cut down to 24.75 inches and chambered as a Robinette-design no-freebore .30BR. I'm trying to get 125gn Sierra MKs to shoot well at 100-300 yards and help use up the copious amounts of quick burning powders in my cupboard that I have no use for - Viht N120/130/133; Norma 200; Alliant re7/10x etc, etc.)