Do you know for a fact that it's a 1/12" twist ?
I'd check it to be sure.
Either way, It'll still most likely shoot either the Sierra or Speer 130gr Spt flat-based bullets. It might also shoot the 150gr flat-based bullets as well as the Nosler 130gr Partitions, which only have a small heel to facilitate bullet seating due to the process of jacket formation that Nosler uses to close the heel on the rear bullet core.
You also didn't say what kind of results you're getting. It might be acceptable or as good as you'll pobably see. You also didn't say what kind of barrel......... Who did the work ?? Why a 1/12" twist ??.
Could it be that the barrel is pitted, or has a damaged crown, or, If it really is a 1/12" twist, my best guess is that it was used with 90-110gr bullets for some type of varmint shooting and the throat is "washed out" from large quantity shooting with large quantities of slow burning powders or--- "shot out".
Have you tried a really, really good cleaning of the bore with a good Cu removing solvent ??? I've got a M98 Mauser in .257Roberts that if kept clean will shoot near 1/2moa, but after 30-40rds will start "throwing" patterns due to Cu build up in some pitting it has mid-bore. (long story- - -).
Questions, questions, questions........