First of all, good luck and hang in there. Sleep issues are so difficult and physically and emotionally draining.
Have allergies or reflux been considered? Allergies, reflux and asthma can be aggravated at nighttime while laying down on a flat crib or bed. Raising mattress or head of bed in addition to meds can help if it is allergies, reflux or asthma related.
Your idea of laying on his floor sounds great. Allows him to work on sleeping independently but assures him you are there. And, eventually I think it would take less adn less time. YOu could also start to tell him you are going to leave for a minute or two but will be right back and see how he handles it.
The first thing we did was to switch to a bed. It didn't solve the problem, but it made it easier for us to lay with our son until he fell asleep. It will also help assure you he isnt going to hurt himself jumping out of the crib. Our son was in a bed before he was 2. He couldn't even walk at the time but it was such a relief for us. When he turned 3 we pushed the issue more and tried more strategies and within a few months he was sleeping on his own.
We reminded him of concrete ways to help himself such as put your head on the pillow/mattress, close your eyes, and no talking. We kept a very regular routine including reading and snuggling and reviewing the things that help us fall asleep. During times he had trouble between ages 3-4, we let him know we would answer any of his calls but he had to stay in his bed. We also would let him know if he stayed in bed for 5mins (or whatever time period)after we left the room we would come back up and give him another hug and kiss. If he got up int he middle fo the night, he could call to us but he couldn't come in our room. If he got up, we would talk to him and tell him to get back in bed and call for us and we would come. If we had to walk him in ourselves, then we wouldn't lay with him. A minute later he could call for us, but he had to call for us and not get out of bed. Through all these intermediary steps he did great. The assurance that we were there and would be there was helpful to him. The consistency of routine and sticking to the plan was crucial, brutal to carry out when we were tired but helpful. From 4-present he really has had only a few hiccups. He is 7 now and is a great sleeper. We still keep a very regular routine.
All kids are truly different. My 2nd son was a great sleeper. He loved his bed, reached for his crib while I tried to read to him, etc. Of course at 4 he now has more hiccups than he did earlier. I am now expecting twins, children 3 and 4 and my greatest hope is that they sleep.
Sleep issues are so tough. Hang in there. Check with your doctor about medical and developmental problems that could be related. Good luck with finding the balance between survival and meeting long term goals of independent sleeping. YOu're doing great in your efforts.