Brett,A couple of thoughts to your issues:
If you are trying to verify the polarity of the Polydomes I would recommend you pull the Polydomes first, note and mark how they are wired, disconnect them and put a DMM on the wires to see if they are wired correctly when speaker is powered. The Polydomes are slip off tab connections and one side is marked red for +. Only pull the crossover if you find a problem with the wiring.
Regarding your Kappa 8’s, you have a bad part or short in there, likely an old electrolytic cap that is now shorting. Was it ever working or did you buy them that way? Hopefully they were working at one time otherwise it could be anything including someone screwing with the internals.
I completely refurbished both a pair of K8’s and K9’s. It is cost prohibitive to pay someone to do it even if you could find someone willing AND capable to do it. Restoring vintage Infinities is a labor of love like refurbishing a vintage classic car. If you can’t or don’t want to do it yourself I would suggest you not go down that path. But at least pull the K8 xover to see if you find something obvious like an electrolytic cap that is bulging or split.
The K9’s are almost impossible to drive due to the woofers dropping below 1 ohm at certain frequency. What I did with good results is wire the woofers direct to the speaker posts, by passing the xover completely and used my Crown XLS in Low Pass mode to push them in a horizontal bi-amp config. So I converted the woofers from passive config to active. The mids and highs of the K9’s are easy to drive. So bi-amping is the way to go with the K9’s. It is a very easy rewire the woofers to make them active and bypass the xover. Wiring the speakers active raises the lowest Ohm drop up to 6 ohms which is a huge difference.
The Crown XLS amps are not musical enough to drive the high ends, they sound awful pushing the top end. But they are adequate to push woofers to good results. Your XLS1500 should be able to handle it. I have two XLS2500's running bridged in low pass mode with each driving one speaker.I actually have to turn them down or there is too much bass.