Newmommy, been thinking about you. Hang in there! Can you wear him in a carrier on your back? I have to do that a lot with my ds after nap when I'm trying to get dinner going, etc. and he will fuss if put down.
I struggle with exactly what you said about feeling that room sharing is the best for siblings, but with 4 yr old dd's sleep issues I am finally considering after two years of sharing that maybe it's not the best after all. Unfortunately now that there are four kids instead of the two there were when they started sharing there isn't really any other choice right now.
Have you considered sensory processing disorder? Both my 4 yr old and 1 yr old have just been diagnosed with this. Or if it's long term and does not resolve as teething or a phase, maybe melatonin? (it's over the counter but not labeled for kids under 18 so would need to be recommended by a dr). My dd just started this ordered by her dev ped and it's been a life changer.
Or it could just be the number of homes. I can't imagine how that seems to a little one. I would probably be screaming all the time, too. Or it could be that he sleeps with his mom at home? I found out after our first two placements when it never would have occurred to me that they both slept with someone at home so my house was probably the first time in their lives that they were put to bed by themselves. Although your dd is in there, too.
But, lack of sleep is really, really hard. Makes it so you can't be the Mom you want to be. At least for me; I get really cranky
It's not a waste of time if he is who God brought to your home for now.
It will get better.