I'm in a simular situation, I bought my boat out of state and there was no title for the motor. Find the serial number of the motor and ask the seller to give you a bill of sale for the motor with the serial number on it and have it notoized by a notory and take it to your BMV for them to give you a title. That's what I have to do in Ohio.
Are you sure you need a title for the motor? In Fl all the DMV cares about is a title for the boat and depending on the size of the trailer you only need to have it registered.
To my knowledge, you do not need to carry either the boat or motor title. Your registration number is on the boat so.. the registration for the trailer is about all you need to carry except maybe proof of insurance.
Contact the DMV in yours state, explain your situation, and see what they recommend. They probably deal with these types of problems all the time and should be able to help you create the necessary documents required in your area.
In Florida, only the trailer and boat are titled. The motor is not. Buying an outboard engine in Florida is like buying a lawn mower. Just keep the receipt and register it with the manufacturer for warranty purposes.