.500 Linebaugh is based on the .348 case, is it not? Why not just go a bit longer and chamber .50/70 for the 2 3/4" case, or maybe a shortened .50Alaskan - or full length Alaskan at 2.090" trimmed, using Starline brass?

That will give you the ballistics you want at even lower pressures.

According to my 2004 Hodgdon Annual Manual, page 111, the .50 Alaskan, with a 22" bl. and Starline brass, will get up to:

:2,089fps w/435gr. LFN w/GC @ 35,500CUP and 1,912fps at only 26,100CUP

:1,940fps w/450gr. Barnes FP @ 35,300CUP and 1,772fps @ 28,600CUP

:1,854fps w/500gr. JFP @ 34,500CUP or 1,719fps @ 28,600CUP

:1,852fps w/525gr. LFN w/GC @ 34,800LUP and 1,724fps @ 27,300LUP

Sounds like a winner to me.