The KH looks to be needing some new tyres shortly and I'm thinking of moving the tyres off the AWD over onto the KH. Are there any issues with doing that?

I put the Yokohama Cdrive2's on the AWD about 15000k's ago based on the excellent experience I've had with the Cdrives over the years on the KH, but I've found that the AWD really scrubs them a lot and I notice that the ride feels a little bouncy on them. I want to try the Eagle F1's on the AWD instead. I've heard really good things about these and want to see how they run on the car.

So, any issues with moving tyres between AWD and FWD? I think that generally uninstalling tyres should be avoided because of the potential risk of damaging them during the process, but otherwise are there any specific issues?

If the rim sizes are the same there is no harm. Requires a bit of labour, swapping tyres off/onto wheels, but if you talk to the shop selling you the Eagles they may be able to do the swaps in one go at a reduced price for the labour.