Thicker oil in that engine wouldn't be my first choice with the tight clearances and narrow passages for the VVT. I'm not usually the guy to say this, but I would sooner throw in conventional oil than synthetic and see if that makes any changes.
Figure out where the oil is going is step 1. Leak or burning. Maybe add some AT205 with fresh oil. I have had good luck doing this for valve stem seals.
A quick compression test wet and dry can rule out the rings. It can be done at home and is cheap and easy. Even if done only on the front bank, you will have a good indication.
The car isn't worth much and the current market is nutty. I would limp it along with any repairs it needed for safety, like the brakes.