I actually think your idea is interesting. Everyone’s suggestions are good but are more about overriding his desire to leave the arena than eliminating it. Your idea fits with the notion of making the right answer easy for the horse, and the wrong answer more difficult (though not scary). An example would be to take walk breaks in the “scary” part of the arena and work harder in the attractive area, like near the barn or the gate.
Warwick Schiller uses this principle a lot. He has a video about teaching a young reining horse to lope a circle by steering it back in when it leaves and leaving it alone when it stays. Obviously that’s a lot more subtle than you’ll need to be for your horse who is actively trying to leave though. There’s a similar idea in this video of teaching a horse to stand still for mounting by yielding the haunches when it moves and leaving it alone when it stands still: https://www.youtube.com/watch?v=cfuRH383Lio. And this “Choose Where You Work and Choose Where You Rest” video might be useful for you too, though I haven’t watched it: https://www.youtube.com/watch?v=nIClBhR3W1M&list=PLRanqnpaErQ5PVpPHRBNwfgs26-EsndmO&index=7.
All of that is to say, I don’t think your idea is worthless. I don’t think the work outside the arena needs to be crazy hard as long as there’s a clear release when he goes back inside. I would expect to have 2-3 rides (or groundwork sessions maybe) in which nothing else is accomplished other than a pressure-release game. It will require good timing and feel, so if you’re not confident you may want to enlist help. Also, if you board make sure that your BO is okay with you working in the areas around the arena (for example, if you would be tearing up the grass or other landscaping).