Hi Giles, Same bike as me - It does sound like an electrical fault - I'd start by spraying some silicone water displacement spray ( on all/any exposed electrical connectors, coil/ht, plug cap, side stand switch, starter relay where the main fuse is, possibly even contacts on the regulator/rectifier under the plastic fairing behind the seat - also the switchgear on the handlebars ( especially the kill switch ). Also worth checking battery connections and earth connections. I'd look very closely at the HT cap - mine runs thru water no problem but if it was split/cracked it could give you those symptoms. Do the lights on the dash go out or flicker when you have problems ?
Let us know how you get on and Good Luck Mike