A lot of people have had good results with Riselone.
I’ve never had a sludges engine but I do use it as regulator maintenance just to help keep everything clean. I just use cheap oil and can get Rislone 1qt bottles for less than a qt of cheap oil costs.
You could try and see if it helps. If so you probably can save the $4k.
Some people, as a last ditch effort, have reported success with using Berrymans chemtool as and engine flush in the oil(1 1/2 to 2 oz per court) put in a cold engine and the idled (not driven) for 10 to 30 min.
If a cleaner or flush reduces the consumption much ya know it’s just caked rings.
As someone mentioned, you could buy a lot of oil for 4k.
I’d try and clean it up and if not just let it burn oil. You might could go a long time still burning oil. The decide on an expensive repair or not