I think I got it to work!
I uninstalled and reinstalled phpbb and the connector.
Before I ran the connector, I had a look at my users to see if there were any usernames or weirdness in the database. I discovered that there were a few users who were awaiting admin approval.
Since I do not require admin approval to be a member, I followed the directions to fix the problem found here:
www.joomlapolis.com/component/option,com_joomlaboard/Itemid,38/func,view/id,6820/catid,10/limit,6/limitstart,0/
So, I synced my users and ran the connector using the LIMIT phpbbgui file. I was able to import about 1/2 of the database with no problem then I began running into the time out problem again. The script would just run and run and do nothing OR it'd save index2.php and phpbbgui.php to my desktop and not import.
I found that clearing my browser cache, cookies, and browser history would allow me to run the script again... but I had to do that before each time I ran the connector. If I just cleared the cache or the cookies, it wouldn't work. I had to do all 3. (Running latest versions of MacOSX and Firefox)
It was tedious but I successfully imported 10,350+ users. New users are automatically updating. Every user seems to be set to her proper user id.
-Khris