A rubber torsionally flexible coupling
is very common on flexibly mounted engines, though the one pictured is very long.
Bash is not correct. If you have soft engine
mounts and a rigid coupling, you have eliminated the benefit of the soft mounts and all the engine vibrations get into the hull
structure. You must align the engine with shaft properly with any sort of coupling, flexible or not.
For those that doubt the efficiency of flexible couplings, we designed two sistership tugboats, around 3500 HP each. One had rigidly mounted engines, and one had soft mounts and a flexible coupling. The noise
levels between the two boats were about 8 - 10 dBA. (3 dBA increase is a doubling of sound levels). Guess which was louder!
I doubt you can successfully glue back the rubber to the steel
. Bonding rubber to steel
is pretty tricky. You really need a new flexible coupling - though you could use a shorter one and a small "spool piece" (a make up piece to take up the extra length) - but it might be cheaper to buy a longer prop shaft than fabricate the custom spool piece.
R&D designs makes them for boats, as does Globe. Google
If you are lucky you might find an off the shelf industrial unit that bolts up with minimal machining required.
I design shaft lines for all sorts of ships and boats for a living by the way