In terms of who you should root for in other games, the main thing you should consider is your TUC winning percentage compared to your winning percentage against teams on the TUC cliff. For example, with Michigan, your record against them is only .5000 . Your current TUC winning percentage is .5200, and to be in any sort of contention for an at-large bid your TUC percentage will most certainly have to be above .5000. So in terms of increasing your own stats, right now, you don't want Michigan to be a TUC. But then again, there is the possibility you meet Michigan in the second round of the playoffs and increase your winning percentage against them to .7500. In this case you would (in hindsight) have wanted them to sweep Notre Dame and first-round opponent in hopes that they could stay a TUC even after losing to you. So it's not always clear in advance which way you would like certain games to go.
(Technically your RPI also fluctuates slightly based on how well teams you've played have done, but the change is small compared to the swing from the TUC cliff, and really only important if you end up in a situation where thousandths of an RPI point would flip a comparison.)
On a slightly deeper level, you also need to be aware of how teams on the TUC cliff affect the teams around you. If Michigan dropped to 26th and UMass went up to 25th in the RPI, it's possible that Hockey East teams you need to pass could benefit more from UMass becoming a TUC than you would by having Michigan not be one. You still run into the same problem as before of not being sure whether UMass being a TUC is a good thing or a bad thing, because that can shift depending on how things go in the Hockey East tournament.
It's also worth pointing out that LSSU is sitting at #27 in the RPI, and Northern already has two losses against them. Anything short of a sweep leaves the door open for LSSU to become a TUC, and since Northern would then have a sub-.5000 record against them that could be devastating to any hopes of getting an at-large bid, even with just one loss in the conference playoffs.