Every state has a method of resolving that issue. I imagine the missing engine issue is why states dropped titling to the engine after '55. The best course of action if your face that problem is to contact your state licensing authority & get the state requirements from the people you'll be dealing with.
The Chevrolet Engine Serial Number became completely useless as a Title/Registration ID in 1957 when the ESN no longer contained a serial number or date (thank goodness - the DMVs that previously used the ESN had caused us plenty of problems).