Hi there
Hard to say exactly what's going on, but your description helps give me a few pointers.
As a vet and long term lamber, I've seen a few odd lambs over the years.
The first thing I have to suggest, given the current climate, is that any lamb with 'neurological' signs, such as the paddling and collapsing, particularly with deformities like the stiff legs, could potentially be Schmallenberg.
Now I wouldn't be too concerned about this, as it seems that once the lambs are born, that's the worst of it over, usually if they're affected badly, they'll not be doing this well, and whatever effects there are now will not get worse, as the main time they are being affected by the virus is inside their mothers.
There are a couple of other causes, such as the occasional deformity caused by other things, including 'daft lamb disease', which might be the case with odd legs and strange brain behaviour, but again, nothing likely to get worse.
I have seen a few texel cross lambs on one particular farm that seemed to do something similar, at first they would collapse to the side, and paddle their legs, but over a few days of nursing, would get better at staying up, and with a bit of walking around, would not be too bad, though on occasion would get overexcited and fall over (the shepherd informed me even at nearly a year old this would occasionally happen!) This would suggest a potential genetic defect, but they grew and fattened just fine, so I wouldn't be worried about it.
There are also nutritional defects that can cause problems, but it is usually in older sheep, though a vitamin injection containing B12 (should be able to get a syringeful just for one lamb from your vet) could help with that, and would certainly not cause any harm.
Otherwise, I think you're doing just the right thing, keep him as calm as you can, help him out with feeding, and keep encouraging him to get up, stand and walk.
As regards the stiff legs, could be part of the general deformity/problems he has, but could potentially be a joint ill, due to having been rejected and perhaps not having the colostrum he should have. I would suggest a full course of a penicillin based antibiotic would help with that (again your vet should be able to give you doses for a single lamb).
Hope that helps, and hope your TLC brings him round
Suzanne