It sounds like there is something marginal about that CPU card. The presence/absence of a cache can affect timings/capacitance/loading of signal lines, so that's a good thing to consider.
The 9500 and the original 9600 have the cache soldered to the logic board and it is not removable, so the presence of that cache could be why it doesn't work in the OP's machines, unless he's talking about a 9600 Enhanced, which is also a Kansas/Mach 5 machine.
On the 9500, removing resistor R31 (IIRC, better do a search first) will disable the on-board cache. The Umax S900 was civilized enough to include a jumper position for this.
Other than the lack of a cache there really aren't any other substantial differences between the x500 CPU slot and the Kansas/Mach 5 slots. I've never actually traced out the slots for the Kansas machine (as I did for the other x500) but the fact that third party upgrade cards work in both means that they must be almost identical. My guess has always been that there's simply more 3V (or maybe 12V) supply lines in the Kansas slot.
If you have an ohmmeter handy, the other thing you can do is check the CLKID pins on your upgrade cards to see if they're all biased the same. This is a little farfetched, but could be a factor if timings are tight. And there were all those upgrades that made us think that logic boards wouldn't work properly above 45 MHz because they had the CLKID pins set wrong, way back when....
You can find the identity of the CLKID pins here:
http://www.io.com/~trag/Apple_pinouts/CPU_Slot_Pinout They're either tied to ground, or (IIRC) floating. In any case, check for connections to GND, 5V or nothing and compare amongst the cards.
If the card works until you install the Sonnet software, then most likely the card has a faulty backside cache chip. The software for G3 upgrades activates the cache (among other things) and the most common problem one sees, if the card crashes when the software loads, is that something is wrong with the cache chip.
I once had a NuBus G3 upgrade from NewerTech with that problem, and when I pulled the heat sink, I found that the assembler had dribbled heat sink grease across the cache chip pins.
If you're really ambitious, compatible cache chips are available from Digikey for $15 - $20 each the last time I checked. I think they're 100 pin chips.