There should be no reason to have to do anything with the Access Points that I am aware of. Assuming they were correctly installed on opposite 120v legs to begin with. Seems like something has changed though since you can now access devices you were not able to before. Maybe something is not on now that was on before. Or perhaps the opposite. A 240V appliance like an electric hot water heater or electric dryer, etc. can couple the 120v phases so if the Access Points are not actually on opposite 120v legs, other things can create cross phase coupling on a temporary basis.
Should be no difference between the EZSrve and the EZBridge. The same 01.60 image.bin file runs in both.
The EZSrve/EZBridge requires a link from the Insteon device as a Controller and the EZSrve/EZBridge as a reponder for it to receive a Group message from a device when the device manually changes state (on/off). The links you describe are going in the opposite direction. Assuming the correct links are present, I think the device view/control screen will reflect the correct status on the next auto refresh. I believe that is why the auto-refresh takes place. Of course you can always request a specific refresh which actually queries the devices (not all devices can be queried in that fashion). I don’t keep track of my devices that way so there could be an exception I am missing.