What are the colors on that back (furthest from reel) switch with the broken blade/contact, I assume (based on the size of the contact) RED+WH and YEL-BL ? If so, that is the issue with the replay award.
Curious as to why the jumper from YEL-BL to the YEL+GR worked though... are there any switch parts laying around, maybe it was marginal and finally broke with all the handling of the reel? And JX should have been unaffected, assuming it's clean and gapped correctly. Both mysteries.
Yes, you're going to need to order a new one. A warning though, this is different from the EOS switch stack on your other reels. The 10K reel has two NO switches, the normal stack (on your other reels) has a single NC switch. Steve will know, based on the fact it's a 10K reel on a Jacks Open.
You should also order a bunch of switch parts (various blades and contacts) to be able to quickly fix these types of issues in the future.