Cheap to try would be the Speer 70gr semi spitzer (supposed to be a stout enough projectile). Some places recommend 1:10 or faster twist but I can find references on the successful use in 1:12 twist.
Not tried them myself.
That the Partiton is shorter than the Speer would then suggest it might also work in a 1:12 twist.
This to give you an idea
Length (inch)
Nosler0.224 60 gr Partition 0.790
Sierra 0.224 55 gr HPBT (GameKing) 0.715
Sierra 0.224 63 gr SMP (Varminter) 0.755
Sierra 0.224 65 gr SBT (GameKing) 0.852
Speer 0.224 70 gr Semi-Spitzer SP 0.808
Barnes 0.224 53 gr TSX Flat Base 0.792
Hornady 0.224 60 gr Spire Point 0.750
Norma 0.224 55 gr Oryx NFI
Reference
https://www.jbmballistics.com/ballistic ... gths.shtml