You could keep him inside and try to figure what's wrong with him, then try to re-introduce to the flock when it's warmer and he's better. Properly caring for sick birds long term is time consuming and mentally draining, so that's something to consider.Anyways, my question is, with all that in mind, should I give him time to get stronger and get them to get along/re-home him, or just put him out of his misery?
I would not try to re-home him because his leg problems and un-thriftiness could be disease related.
Euthanasia really might be the best choice for both you and the rooster. I know it's a hard decision to make, and only you can make it. FWIW, any time I have euthanized one I have never regretted it, and as horrible as this might sound to some, I have felt an immediate sense of relief after doing it.