It drives me crazy that all of the states seem to be different in how they handle motor vehicles. Whether it's a car, truck, motorcycle, boat, trailer, quad, etc. There should be some standard or national titling system so it's not this difficult. NJ has titles/registration for boats (13' or longer, nothing for motors) but with a trailer, it has to be rated over 2500 lbs to get a title otherwise you just get a registration. And it's very difficult to claim or takeover something a previous owner may have abandoned. A notarized bill of sale is a must but even that is often not enough. I won't even mess with anything that doesn't have good, clean paperwork anymore. I wish the OP the best of luck, but without a title it may be very difficult if not impossible to get the boat titled and registered.
On a side note, these newer electronic signatures are cr@p. No matter how hard I try to sign properly with an electronic pen, it does not look close to my real signature so I don't think these are going to make things better, probably make it worse.