We've been playing with permutations to try to recreate your issue, but have fell short in being able to pinpoint exactly what is happening.
If you are going to flip hosts, make sure that you use the
UBB.threads System Requirements Test to ensure that your environment has all of the capabilities needed to run UBB.threads.
I have a listing of recommended hosts that I have worked with
here (note that my affiliate code with these providers is sent with each offsite link). isaac uses BlueHost Pro Shared Hosting, and I use a StableHost 4 slice VPS.
The documentation isn't out of date, a security setting on some servers (I believe it is a setting in
SuPHP) will throw an error when a script is executed in a folder chmodded 777 or the script's chmod is set to 666; simply make sure the folder holding threads is chmodded 755 (and the admin folder) and that the ubbthreads.php and file is 644.
"Technically" the only files that need to be 666 are in the /cache_builders/custom, /includes, /languages, /styles/, and /templates/default/ folders, as these are the only ones with editors in the control panel (note that the /templates/compile, /templates/default, /cache, /includes, /session, /styles, /gallery, /uploads folders all need to be 777).
ModSecurity is a PHP Security module that has some rather strict default rules that can throw 403 errors as well.
What are the permissions on your /images/captcha folder and its contents? Is this a CPanel server? (time to grasp at straws)