To answer your question, there is no limit on how long they have to respond. In fact, they are at liberty not to respond at all or ever.
You really need a lawyer. Unless you hire one, you are at the company's mercy because the status quo favors them. They have no real incentive to act without a legitimate threat of legal action.
This is definitely a case where you need to consult in person with a consumer attorney. You do not have to allow them to replace the engine and they can be sued for the amount it will cost to replace the engine and your rental expenses. The attorney you hire can add a request for attorney's fee to any lawsuit filed since this is a breach of warranty claim.