something like an option / preference "don't close TBB when Firefox closes" sounds like a solution. Technically, it'd be "don't close Tor / Vidalia" wouldn't it, because "TBB" includes Tor?
Firefox in TBB is dependent on Tor, but Tor (in TBB) doesn't necessarily have to be dependent on Firefox running.
Installing both,& running one, shutting it down, starting the other is doable, but kinda pain.
Alternatively, as a hackish fix, you could modify your "permanent" installation to bind to ports that won't conflict with TBB. Off the top of my head, I think you'd want to pick non-default values for ControlPort and SocksPort in your torrc (with matching values in Vidalia), as well as a non-default value for proxyPort in Polipo's config file, and changing socksParentProxy (also in Polipo's config file) to point to the new value you've given to torrc's SocksPort.
I don't have TorButton to fenangle with on this computer, but I'm sure somewhere in its options or in about:config you can change the port it looks for Polipo on, or plug it directly into Tor's socks port if you're not using Polipo.
The ultimate goal here is to have your "permanent" installation of Tor/Vidalia/Polipo/Firefox/Torbutton use a completely different set of ports than TBB. Like I said, hackish, but the result should be worth it if you use both often.
~Justin Aplin