Keri,
I changed my iRATs so that I don't have a firm time limit. I give a suggested time, and I let it count down so that everyone can see it, but when that time is over, I ask if anyone needs more time. Usually a few students need or want a bit more time, but they seem to get the message that they need to finish quickly because the rest of us are waiting. For the tRAT, you could do something similar. I also know that some teachers wait until 1/2 of the teams are done and then announce that there are X minutes left. This again helps to prop the slower teams along without having a firm time limit.