FIXED IT!!!!!
I'll document this here so I can refer to it if it ever happens again:
I decided to try installing Adv BBCode Box to see if maybe that would bypass the problem (it didn't). It's an extension that gives you more control over BBCodes and I installed it when it was mentioned by the host's tech support as a possible problem because he thought I had it installed.
But in the process of installing it and testing it, I wound up reading a post on their support forum where someone mentioned an issue somewhat similar to ours, and that led me to the solution.
For some reason, even though all previous settings transferred over from the old BBS, one setting was reset, and that was the culprit.
It's in the General > Post Settings section of the phpBB ACP. There's a setting there called "Allowed schemes in links".
This was set to blank, but by default it should be set to "http,https" (without quotes). This allows only http & https to be used in URLs in links.
![Image](http://www.soldcentralfl.com/bob/schemes.jpg)