Don't leave it strapped for too long. It needs to build some strength back into it. The strapping might be restricting it too much from allowing it to strengthen. That being said don't go cold turkey and run for 3 hours in the hills without it. Start by doing a couple of short ones during the week on easy terrain and before you know it you will be back in no time at all without it!
I can't even walk properly unless in supportive sneakers! Sounds a scary prospect! But I do know what you mean. Perhaps I should start with doing some more walking first...
It still swells up pretty large even with no exercise which is fairly yuck :-(
A few random thoughts. Not professional medical advice.
Apart from being tedious it's good to start with walking with short bursts of gentle running, on the flats/roads, and gradually upping the run side of the ratio.
If you're already comfortable running in terrain as long as the ankle is braced/strapped, definitely do any non-terrain running 'unprotected'
While it sounds like you might basically need to strap for any true terrain running 'for ever' now, aim to also gradually work up in roughness what you are happy to run unstrapped (eg, road->grass->less groomed grass->trails....)
The hardest thing: Be Patient!