probably 584x29 or 584-29. That's consistent with a lot of 831 models, as is the M-645-114 payout disc. Many 831 models used the same index disc on all three reels.
afaik, bally didn't make a skill stop machine. However, if they did, if would have been for a non-usa market and I have a lot less info on those machines.
can you post pictures of the payout counter showing the wiring and all sides of the reel mech? If the site is not letting you post because the pics are too big, please email highest possible resolution pictures to slotpics@cdyn.com. File size as huge as you want :-)