It seems to be that the general consensus of the panel here is that there will need to be some sort of IR translator bought and installed, is this correct?

Can someone explain to me why there are several different TV makes and models that are experiencing the same issues?

Buzz,
You are correct on your thought process that we are out of unique pairs of TV's to put into rooms. I have already tried to swap TV's from other rooms that don't have like pairs. In some cases, even swapping out different brands, makes, and models, one can still put a TV back into the same room that creates the same issue. Example: 105 A and B are not having a problem. Take 105 B TV to put into 218 A, and it doesn't fix this problem, or creates a new one in 105B.
This facility has no TV policy or program and the resident's themselves (in some cases) are asked to bring in their own TV from home. There's no way to guarantee that if/when we have to remove and replace a TV that we will not generate the same problem, even if one didn't persist in a certain room in the first place.

Is there any way at all to start troubleshooting this issue by taking the affecting remote around to different TV's within the facility? IE, if remote 105B turns off multiple TV's throughout the facility, it would stand to reason, that each of those TV's that said remote turns off/on and controls volume, would be the same problem if brought to room 105B. Is this correct?

We don't have any sort of system in place like Buzz spoke of in his post, and really no plans to implement one. It would be a costly venture, and one the facility would not entertain at them moment. So, I need to create a viable solution to correct this issue for not only the rooms that have issues now, but for the ones that WILL in the future.