We are not ready to put him down,because he is still a happy boy despite all this. But I am looking for solutions that will help him be comfortable and not fall over, especially at night. Neither one of us is sleeping and he can't be left alone at all.
I don't really know a nighttime solution for this situation. You kind of end up just needing to turn him to his other side every few hours and keep him on soft, dry supportive bedding. He may actually adjust to the new normal...my dog did. It does affect your own sleep, but if you can just get to where you flip him and you both go back to sleep, it will become more doable.
One possible consideration if he continues struggling to get up is to see if you can find an arrangement where he feels more secure, even though lying down. I am not sure where he sleeps, but as a dog he may have some kind of instinctive fear of, for example, lying in his bed on the kitchen floor, and not being able to get up because he feels vulnerable to dogs/predators in his wiring for survival. Possibly he will accept lying down at night better if he is up higher, or in a covered crate that feels safe to him, or in your bed.
I really like a playpen or baby crib for a dog with mobility (or incontinence) issues. It is safe, clean, and you can put it next to your bed at night so he's only a step away. If he is a heavy standard dachshund, I would go with the crib where you can lower the side and save your back (if you're sure he can't climb out of it). If he's a mini or you are young and strong, a playpen would be good. Even if he adjusts to understanding he can't get up without assistance, I think you are going to want to turn him in the middle of the night if he will accept that. Some dogs insist on lying only on one side. It's just kind of a difference to think, "Oh no, I'm in the middle of the floor and I can't get up to run or fight," versus, "Oh, wow, I'm sleeping next to mom in this comfy bed, Night-Night."
The first few weeks after your dog goes down seem the most stressful. I remember how it was when my big dog first went down, the stress. And he barked all night for a while. But it got better after a couple of weeks. During those first couple of weeks I was pretty frazzled by worrying about him and getting no sleep.
I'm not sure what kind of PT your dog has been doing, but swimming would be great at this stage if he can do that. If you have a yard, you could get a cheap wading pool and let him paddle around in the back yard.