Well, you can indeed run those just like I said, but that would get you a situation in which both amps are on all the time. If you want to be able to use the TR for cleans
only and the BJr for dirty
only, you'll need what's referred to as an A/B switch (which allows you to play amp a OR amp B), or if you're really adventurous, an A/B/Y (which allows you to select amp A, amp B or BOTH)
http://www.framptone.com/
http://www.tonebone.com/re-bigshot-aby.htm
A couple samples of A/B/Y, though a simple, passive A/B is a reasonably simple build if you're inclined. This may not alleviate your pedal problem, though.