Repair complete!
I ended up using Digikey part
102-1768-ND instead of the one from Mouser just because I was already making an order from Digikey at the time.
I desoldered the broken encoder, added in the new one and confirmed that it works just like the old one. I knew for certain that the original encoders had 20 detents per revolution, and I even spent a few minutes searching for encoders that might have 20 detents with 24 ppr, but it seemed to me that with encoders such as these the number of detents matches the number of pulses that you get.
20 detents with 20 pulses per revolution was indeed correct; it never skipped a value on either the course or fine adjustment settings. Something that I did notice that was slightly different was that the encoder that I chose has a more "muddy" feel to the detents where as the original encoder has sharper detents that are more defined. One other difference is that the body/base of the new encoder is very slightly narrower than the original, so when I placed the new encoder onto the board it sits maybe a millimeter higher above the board than before. This doesn't cause any problems in operation though.