Nobody knows what the cause is. Not everybody wants to rebuild the engine. Others can't get help from incompetent dealerships or their clueless techs. The threadstarter also stated that the vehicle is a salvage which opens up another can of worms. And, salvages are there for a reason, and rarely will come with a history of maintenance either.
What choices does the threadstarter have at a salvage car budget IF the issue isn't addressed by the dealer?
PCV---- no brainer. If the old PCV is sludged/crudded whatever, then you need to pull the oil pan and valve cover for inspection and cleaning.
Synthetic oil... no brainer. Problem is that some think that it alone allows longer oil change intervals. It doesn't. Synthetic oil is not a fix-it-all.
Thicker oil. Less will squeeze buy. Again, no brainer and wonder why people resist this one the most. Grade is proven by too many to lower or reduce consumption. Its a 1st step attempt.
Oil level. Must be checked often and kept to the FULL point always. This is beyond too many consumers' abilities and I just don't understand why. Stupidity? incompetence? Blind faith or trust? By far, the biggest engine killer that I regularly see is LOW oil levels, usually combined with skipped or negligent oil change intervals.
5-15 minute cold engine flush. If there is excessive crud/sludge, you might want to avoid this one because too much can be released all at once. So, just wait just after 2-3 oil changes intervals, see what comes out, inspect the engine, inspect the filter pleat contents.... then consider the flush.
Yes, oils do clean. Conventional oils do clean. All have detergents/dispersants which varies among spec and marketing that the oil meets. So, don't rule out HDEO oils, even though many HDEO, like PCMO, are moving toward greenie additive packages that are as good as they claim.
Filter inspection... at every oil change, one needs to inspect the filter contents to see if there is anything going on or not.
Don't run to dealer crying about oil consumption when you have a salvage vehicle, unknown history, unknown recalls still pending, .... You have to move this along slowly. Get 3-4 oil change intervals in. Keep driving and keep that level full. See how the dealer reacts to 'recalls' needed 1st, if any. Do any/all maintenance based on mileage/time on vehicle, and common sense. Create those records. Then in a year or so, when you verifed all sludge clean out, if any, when you several oil changes, when you have all maintenance done, try to see if they ignore the 'salvage' aspect or not.
Like the 5-15minute flush, there are oil additives that can be used for the full interval. Again, once needs to know the buildup level before adding anything. So, don't jump on the oil additives, like BG MOA, Rislone, Marvel, Lubegard, STP.... until you have run thru some inspected oil change intervals. Then you can pick one per interval and see what happens.
Typical, when you have excessive consumptions, you are at the hope and pray. Hope and pray that something works. Or, hope and pray that an automaker ignores the inch of sludge in the engine, or the fact that its a salvage. How many lotteries have you won? Keep hoping and praying all you want. Do something NOW and keep doing something. Most want to start threads, do nothing, and then whine and cry about the cost of their engine replacement on a forum.