As aviation organisations go, BMAA paperwork is one of the less painful.
I'd think that with the parts, a capable assistant, and a winch, I could probably change the engine in a weekend - but it won't be a cheap exercise when you add up all the small bits you need to change.
In my opinion - just go shopping for an AX2000 with a 582 on it already, unless the HKS engined one is a particularly nice airframe for a spectacularly low price.
Or an X'Air/582, which in my opinion is still the nicer aeroplane - albeit without a source of spares in Rochdale.
The 503 is arguably an even more robust engine than the 582 - it's just not so well supported now, and really needs an airframe as lightweight as an AX3 or Thruster TST to be viable. On an X'Air or AX2000, it's going to be gutless.
G