OK. Fixed it on my sites.

Posting here, if anyone else is looking for a simple and effective solution.
I simply added a "max-width:560px;" to the ".post-content" section in the CSS.

This only will break strings of text that are longer than 560px. The rest of your
text will naturally break where they are expected to break.

If you have users posting unnaturally long numbers or strings of DNA-code that
push your discussions off the page, this fix could be exactly what you're looking for.

I will admit, it's a "dirty-fix," and there is probably a better way to do it, but it does work.
And you wont be waiting another 5+ years for an official fix.

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BTW, The stock ".post-inner" CSS already takes care of overflow with
display: block;
max-width: 100%;
overflow: auto;

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If you wanted to take things a step further, you could inline the CSS style to your
post_side.tpl and post_top.tpl and have it dynamically add the max-width
of any long unnatural/unbreakable string (or url) according to the "Medium Image
max-width/height in pixels" setting of Control Panel > Gallery Settings

NOTE:
since UBBCentral has yet to fix this issue on their support site (here), I intentionally
shorted the above lines for readability without needing to over-scroll.