So here's what I found:
Obviously that big "missing tooth grin" isn't what it is supposed to look like! Amazing the machine was "kinda working still" - the coupler was completely broken in to two pieces, but I guess the broken halves were wedged together to some degree. Circles were machining with two "kinks" in them when the two major Y-stage direction changes occurred, but other than that it was still running fine! I think I ran for a day (about 5 hours of machining) before I finally was SURE something was wrong and stopped to find the cause! I was llucky that the precision on the parts I was making meant it didn't end up mattering.
For Mikini owners, here is the location of the Y-axis limit switch - it is under the "way protection" shields (4 screws hold that on at the front edge, and two VERY hard to reach ones with nuts on the back side (tricky!) hold on the operator/back side):
Also, I was surprised at how much debris still gets underneath those protectors. The motor and the guides have cutting fluid and chips on them. Clearly they are WELL protected, but not 100% (I guess it is possible the stuff gets there from underneath by splashing up or getting blown in there when I clean that area, need to keep that in mind from here on out! Here you can see the coupler in 2 pieces, and how to remove and replace it (let the machine cool down first, the motor is HOT!!!):
I was unable to find the same coupler (my guess is these were made in China with the machine, as they don't look like the highest quality parts and this part broke with a brittle fracture so in my opinion it was made from the wrong material). And the shafts are different sizes. The motor is a 1/2" shaft with a 5/16" key (there was no key installed). The screw shaft is 10 mm (0.394") with a flat ground on it. Both shafts were "clocked" using a very small setscrew in the coupler.
I purchased Huco Aluminum Oldham couplers from Amazon (Huco Oldham Coupling, Aluminum, Inch: Sliding Block Couplings: Amazon.com: Industrial & Scientific). I got size 41 couplers but had to turn the OD down to fit in the tight confines in the Mikini (I clamped the coupler to a shaft and put it on the spindle, and used a mill tool in the vise like a vertical lathe, and turned the OD down. The Delrin piece I just sanded down. Had to do all that with the X-axis as my Y-axis was out of commission, obviously!). I don't think size 33 would be large enough to span the length required. I keyed the 1/2" coupler properly with a broach so I could key it to the shaft. For the 10 mm shaft I put in a larger set screw to clock it.
Hope this helps someone in the future!