I've been beating up my Vista64 laptop to get it to work like I want.
After many, many attempts, clicking on a link in Thunderbird Portable would start a clean install of Firefox, and not start my own Firefox Portable. Of course, if Firefox Portable was already running, there was never a problem.
It seems that Control Panel / Default Programs / Set Associations / Protocol (not the file types portion of the listing!) only allowed choosing Firefox or Internet Explorer with no option to "browse" or search for other programs. This affects the HTTP and HTTPS protocols.
After running it, the Protocol handlers list now includes Firefox Portable and allows me to choose it. Now the laptop works the way I want.
I thought that this might be of some value to others here, as this question seems to come up fairly often in this forum. Sorry if there is a question about portability of this solution.