WOW......................50k miles and that kind of oil usage. Our 05 at 61k uses 1 qt. roughly every 3k. I run Mobil 1 which has been known to burn in some motors, and not in others.
Several folks have had valve train issues such as failed rocker arms and valve springs with the 3.8. If I were you, I would pull the valve covers to be sure you don't have a much simpler repair that can be done without engine removal.
Its also a shame that the 06s did not have the 7/70 power train warranty, as your bill would not exceed $100.
These Chrysler engines including the 3.8 are pretty tough for the most part if you keep enough oil in them and don't run them like the Indy 500.
I just bet you might have an easier repair that you think. If not, with that low of mileage you will want to spend enough to put a good motor back in there so it will last you a good long time..
2011 Mineral Gray Hyundai Santa Fe GLS AWD 3.5L V6
2014 Billet Silver Charger R/T AWD
04 Flame Red 5.7L Durango SLT