They do have some good points, and I have never regretted going down the Champ path.
From the pics 2k is about $1500 too much.
Your main supply of parts would be in the UK, which is going to factor heavily in the cost of parts. Nearly everything is still available, mostly NOS, some repo.
Rusty sills are a common problem.
The motors are a B40 Rolls Royce (made under licence by Austin) and are generally a long lasting unit, fully waterproofed, which also adds a little complication.
Torsion bar suspension all round, which provides a comfy ride, but there are a lot of moving parts to look at during a rebuild.
Transfer case is integral with the back diff, it is not of the High/low variety, but supplies a change in direction: giving 5 forward and 5 reverse gears.
Most back diff problems were resolved during service life ( I see they are military, not the rarer civilian model).
I could go on for sometime, but I will spare you. Yes they are a complicated little beasty
but I imagine a right hand drive Rolls Royce powered convertible will help you stand out from the crowd, but there will be a fair bit of work involved.
If you have the vehicle No. (on Brass plate, upper firewall under the hood, passenger side,) you should get a little info from the register:
http://www.austinchamp.com/
Not to mention a full history of the Champ in general.
Just to show what waterproofing was for:
http://www.youtube.com/watch?v=_VLTlMr7qYk
Let us know what you decide.
Rich.