Finally got a time window over the weekend to reinstall the pfSense. This time, I went through the process as suggested by DAVe3283 and akuma1x. The details are below.
First, on the pfSense, I setup DHCP static addresses for the AP's and the controller PC using their MAC addresses.
Next, prior to shutting down the Untangle Firewall, I factory defaulted all of the AP's from the Unifi Controller software. Once they were all defaulted, I removed power from the AP's and also removed power from the ethernet switch they were connected to. Not sure if removing power was necessary, but, wanted to make sure the AP's would boot up and get a new IP from the pfSense with no issues.
On the controller PC, In the Unifi Controller software, made sure the gateway setting and network settings reflected the new network information: 192.168.14.1 and 192.168.14.x/23. Powered down the Unifi Controller PC.
Shutdown the Untangle Firewall and connected the pfSense Firewall in its place and powered it and the ethernet switch up. Used my laptop to connect to the webUI of pfSense via the ethernet switch. After the pfSense Firewall powered up and I could see that all interfaces were up from my laptop, I powered up the Unifi Controller PC.
The Unifi Controller PC booted up and got its new IP. In the Unifi Controller software, I adopted all the AP's one by one and verified they received the correct IPs and were "Connected". They were consistently connected for over an hour with no further issues as I'd had in the previous install attempt.
Verified client PCs were connecting the the APs and passing traffic successfully.
Started fail-over testing by disconnecting WAN1. Made sure internet traffic was flowing through WAN2 and then back through WAN1 when I reconnected WAN1. It did, and I was impressed at how fast and seamless the transition was!
After a couple of days, everything is still working great. Thanks to all who submitted suggestions - this one is solved!