Take a look at how the current opener is installed. If it's anything like
mine, the only real differences between a motor replacement and a complete
replacement are the 3 lag bolts where the rail attaches to the header and
the 4 bolts used to connect the 3 rail sections, making it one long rail.
Everything else will need to be taken apart anyway, so there is not very
much worked saved by replacing just the motor, assuming you could even find
one to match.
In addition, I doubt you'll get a warranty if you mix and match parts.
Finally, look at the newer options available (belt drive, screw drive,
etc.) GDO's have improved significantly in 20 years. I suggest a complete
replacement to ensure that there are no mix and match issues.
Here's a trick that I used when I hung my GDO. There is a room above my
garage and the noise from the GDO was transmitted through the joists when
it was hung directly from the angle iron that spanned the joist opening. I
hung the GDO from 2 pieces of conveyor belt material to isolate it from the
joists. It cut the noise by about 75%. It used to wake my kids up but after
I added the rubber hangers they slept right through the noise. It's been
hanging that way for more than 20 years.