Thanks for all the advice!
I replaced Q24 and got everything hooked back up. Everything "works," but I put that in quotes because it's still not quite right.
The right ramp flashers (of which there are three - the green dome up top, under the ramp, and in the backbox) now flash, but they are much weaker than every other set of flashers. They flash in test, but they are very dim, and sometimes fail to pulse at all. If I go to the "All Lights and Flashers" test, which is supposed to pulse all flashers dimly, the right ramp flashers do not illuminate at all.
What could cause this to work, but be weaker? Replacement transistor was faulty? Could I have made a mistake somewhere that could cause this?
The Rottendog board is a bit different from the original, and I don't know if there are any special considerations I should be aware of. For example, most odd numbered transistors (Q19, Q21, Q23...Q53, Q55, Q57) do not exist. Instead, there are some small flat components (possibly surface mount resistors) on the backside of the board bridging from the 3rd pin on the TIP102 transistors that weren't present on the original board. Could my dim flasher problem be due to this resistor? Due to the very small size of these components, it was very difficult to tell if the proper connection was made. Wish I'd taken a picture while I had the board out.