I contacted a pro carpet cleaning crew. They advised we needed to get virtually all the oil collected before cleaning could be effective. No suggestion on how to do it other than hot soapy water and blotters. After 3 repetitions, it's already getting old with many more treatments yet to come.
They also counseled that if there is a wooden floor beneath the carpet, installing new carpet would not solve the problem. Eventually oil in the wood would migrate up and collect soil on the carpet and make adjacent wood surfaces (steps) slippery. If the subfloor is fiberglass (which it is) the old carpet and adhesive can be removed, the surface cleaned and new carpet glued in place.
Fortunately, my wife is a genius at removing most stains, including wine on carpet, but an oil spill she can't fix.