Thanks to 5Z and Roy B. for their help. I adjusted the FLARM configuration file:
-My config file already had "$PFLAC,S,OWNMODEC,0", but I noticed that I had:
$PFLAC,S,MODEC,1
so I set it to:
$PFLAC,S,MODEC,0
-Per Roy B. I cleaned the FLARM SD chip and put only the latest firmware update and the config file
-I also made some adjustments to the transponder configuration to correct errors found on the PAPR report. One of those was that the aircraft ID was missing the "N". I corrected that in both the transponder and also the FLARM.

I don't know which of these changes fixed the problem, but I tested the system yesterday and I am no longer getting the conflicts.

Thanks again for the help!

Rich L.