does anyone have any advice on the best method for removing the valves from the barrel

Yes.

Take off the exhaust.

Remove the pulley wheel - it's reverse (or left hand) thread, so don't break it trying to get it off the normal way.

Remove the circlip.

Screw the nut and washer back on to the shaft.

Use something to heave on the end of the shaft - I use a claw hammer and rag and lever the thing out.

It may be very hard to remove, but it is simply carbon build up - there's nothing else holding it in there.
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Go carefully with Dave's method. i'm sure that it works for him, but it's quite easy to bend the shaft, which could cause it to bind up upon reassembly.

There are proper tools available which are no fuss.