>     The telescope has two axis of rotation, R.A. and Dec. The encoder on
> R.A. axis is attached to a large ring on the telescope mount, by a toothed
> belt, giving a ratio of 300:1.... thus the encoder produces 1749600
> pulses/revolution... or 4860 pulse/deg.
>     The encoder on Dec. axis is attached to a smaller ring on the telescope
> mount, by a toothed belt, giving a ratio of 100:1.... thus the encoder
> produces 583200 pulses/revolution... or 1620 pulse/deg.

What is the maximum rate that you can expect? You can just poll the
encoders during a timer-based interrupt quite frequently, 50k per second
or more, and not have to deal with any messy external parts. If the data
rate is low enough... Testing for overspeed is easy to do within the loop,
so if you are not sure, just write some test code, hook a PIC to the
encoders, and run the scope as is to see if you overrun(both phases of an
encoder change since last check), then turn on an LED or something...
That'd at least give you an idea if it's going to work. If you have 6000
pulses per degree, you could swing that telescope 8 degrees per second
without an overspeed error at 50k interrupts per second.

-bob