What do you think about changing the forums so that when you reply to a post, hit the reply button at the bottom, the blank reply box opens in a new tab?

If you hit command-Reply, the blank reply box opens in a new tab (Edit: assuming that you've got the pref set in Safari > Preferences > Tabs).

Edit: Thinking about it, opening the reply box in a new tab would be helpful in instances in which I need to refer back to posts in a thread other than the one to which I'm replying.

It's already a browser option. Why complicate and/or duplicate things?

One less step for users.

Edit: Two less steps, possibly many, actually, because if it were built into UBB.threads the extra tab would (ideally, anyhow) close on its own when you hit "Submit", and, further, you wouldn't have to close and reopen the reply window every time you needed to refer back to the original thread.

One less step? Not by me. My browser is set to open a new tab by holding the control key while clicking on the URL.* One step. And it's obviously optional. Ergo the best of both possible worlds.
(I could also opt for automation by selecting that option [new tab or new window] for every new URL.)

* I use this option primarily while reading newspapers in order to check out individual articles while retaining the main page.

If it were automatic in UBB.threads you wouldn't have to hit control (or, in my case, command), ergo, one less step.

Yes, but then everyone who did not want another open tab would need to close the original tab, which would require two extra steps: making it the active tab, then clicking or typing command-W to close it.

Good point!

I think the best approach is to simply use command/control-click to open a new tab when you want one.

Edit: But that adds perhaps the most difficult step of all...remembering to do it.

Well, it's a browser option, but my browser (Firefox 39.0.3) is already set to "Open New Windows in a New Tab" and it doesn't work when I click on the Reply link.

Sure, I can click on the right button of the mouse for the contextual menu, but that's one more thing to remember.

It is technically possible to modify the forum software to do this, but it's not (easily) possible to make the new tab close automatically when you hit Submit.

I'm also concerned that a lot of new users might think "hey, waitaminnit, my page disappeared!"

You're right. I just tried it and got a contextual menu.
Now try holding down the ⌘ (command) key and click on the Reply link. It should work perfectly.
Sorry for not testing that out earlier. It seems to work on the other links as well.
Side note: Doing that for a reply gets the job done, but reverting to the original tab obviously will not show the Reply or Edit until refreshed. Confusion could be the outcome of choosing such a method.

That's because that setting only instructs Firefox to open a new tab instead of a new window in instances in which a link is written to open a new window when clicked. If the page source code does not specify that the link open in a new window, it won't, unless one of the keyboard/mouse shortcuts described above is employed.