This is a really common problem that comes from some really common mistakes riders make.
NO! He is not 'napping', nor is he tired or sore or anything but getting spoiled. He is 'stalling out' and losing forward motion because he wants to go out of the gate. That is why he is speeding up going toward the gate and stalling out and trying to NOT leave the gate area.
A rearing horse is always a rider error until it has become a habit. Then, they will rear because of a previous rider letting them lose forward impulsion.
NO! Disengaging his hind quarters is not going to stop this unwanted behavior -- as you have found out. It takes a more serious form of 'negative reinforcement'. He quite simply needs his butt spanked and be made to go faster away from the gate.
If you had popped him a good one on the butt the first time he tried this, it would have discouraged the behavior back when he was first thinking about leaving the arena and its work behind him. Now, he may fight you to maintain the status quo. Some put up a pretty good fight because their rider has accepted the behavior. So, not knowing how old you are or how good a rider you are, you may need someone else to get on him and straighten him out. If you do this, he will still 'try' you, but he will quickly straighten out as soon as you get after him.
This is a very common 'vice' when riders do not know how to prevent a horse from disliking their 'work area' and allow them to think that rest, relief, removing all pressure and only 'good' things happen outside the arena and only work and drudgery happen inside the arena.
There are some things that ALL riders can do to prevent this kind of behavior from starting in the first place.
1) Rest a horse often in an arena ONLY when the horse is doing things well and wanting to go forward freely. Then, rest him at the point farthest from the gate. Or, if there is a particular place in the arena he tries to avoid or is afraid of, simply rest him there. Rest in the arena is the only reward he needs for doing well.
2) When you are ready to leave the arena, never ever let a horse just turn and ride out of the gate. Always go past the gate (preferably to the farthest point from the gate), stop, stand him still while mounted for at least a minute. When, AND ONLY WHEN, he is relaxed and standing still on a loose rein, get off, loosen your girth and lead him out of the gate. Again, reward good behavior.
This is how I have made my students and 4-H riders quit each riding session for more than 40 years and not one has had a horse get gate sour. They NEVER are ridden out of the gate.
[I also do not let riders stop near the gate to visit with people standing along the rail.]
3) If you are at a show and must ride out of the gate, ride your horse directly to a work area and work him hard. I prefer to work a horse harder outside AFTER a show class than he did in the ring. Then, at the far end of the work area (out of the way of other riders), stop and rest the horse on a loose rein for at least a minute (5 minutes is better), then get off, loosen the girth and lead the horse back to his stall or trailer or wherever you saddled and got him ready.
You must reward good behavior and never inadvertently reward unwanted behavior.
You must never let a horse decide when he is done working and never let him decide where he wants to go. You have to call ALL of the shots.
This will escalate if it is not addressed immediately.
Good luck and ride safe.