Hate to suggest this, but low oil pressure is often caused by excessive main and/or rod bearing clearances. 3.8s are sloppy to begin with. Has this engine ever been run low on oil?
'09 JKRU. 4" Teraflex long arm, Teraflex R44 housing, Teraflex / Fox Resis, Poly skids, Nemesis Billy Rockers, Nemesis flares, 37" ATZ P3s on 17" 5x5.5" Trailready HDs, Spyntec hubs, Yukon Hardcore lockout hubs, Teraflex BBK, Mopar BBK master/booster, Superior front & G2 rear axle shafts, CTMs, Reids, Synergy drag link & tie rod, 5.38s, TF Dual Rate front bar, TF bumpers, Warn Powerplant, Tom Woods shafts, AA xfer case cable, Kilby canister relo, RH4x4 cage.