Title for car where engines are swapped

[50Trucking]

I am in Florida. I just purchased an A model that was under restoration when the owner died. The car came with a title from the seller's widow. The deceased had the engine completely rebuilt by a reputable builder.

The car is not a good candidate to be restored to a very nice car however it can be reassembled into a good driver, that will be presentable.

I have an good engine that I purchased from a guy that bought an A and just used the body for a Hot Rod and sold off the drivetrain parts.

I want to put the used engine in the car and save the rebuilt engine for another project.

This brings me to the questions. When I change the engine, the serial number on the Title will not match the car.

When I put the engine in another car I am building from spare parts and pieces, which has not been titled "Bill of Sale only" The engine number will show up in the Florida records as belonging to the other car.

What do I do about this? Do I contact DMV and tell them I am changing engines and need a new title or what?

Then what do I do about the other car when I get it put together and ready to title it.

Should I grind off the numbers on the two engines and swap the engine numbers. Can this be done.
This has to come up in the A model World all the time as engines are replaced frequently but I have never been in this situation.

Your help in steering me in the right direction is appreciated.