I'm going to put this down as the solution.... Wasn't the most definitive outcome....
I paused the two rules I had setup to change modes, tested button presses and was still seeing triple events recorded, though weirdly no temperature or battery events recorded over at least the last month.
I did the re-pairing multiple times (poking a pin in the rest hole on the back for 4-5 seconds while HE was in pairing mode). It picked up the previously paired button device, with the link to the HE device. I pressed the configure and reset commands multiple times, each time it would report battery and temperature, though the temperature was wildly innaccurate (26+C and we are only in the second day of Spring).
For a good 20 minutes or more any press or hold of the button would not be detected, though throughout this time I was re-pairing and re-configuring the device multiple times. I was about swap out the device in the rules for a virtual one while I removed it from HE and re-paired as a new device, but decided to check out the Zigbee map before I tried this. I don't expect this was what changed things, but it eventually showed up routing through an IKEA repeater downstairs in the garage, odd choice I would have thought. It then suddenly started detecting presses and holds. Must have been taking some time to find a good route. Perhaps I need to adjust the power on the hub, which is currently set to 8.....
Either way, very happy to have it sorted out now. One more button to fix.... I think.
Thanks for the suggestions.
