My 2c, do you see anything else occurring at the same time? i.e. instruments behaving strangely? I know you've looked at the electrics but it might be worthwhile having another look with the engine running. Remove the fuse cover and wriggle all the relays and fuses as well as all the wires feeding into the fuse box and see if the engine stumbles. It's possible that a fuse/relay/fuse holder is not sitting snugly or has a hair line crack. I mention this because I've suffered from all of the above! The amount of vibration and its effect on the electrical system cannot be under estimated! Given the starter motor is also causing problems I'd be making 100% certain the main fuse (inside a little cover next to the battery) was firmly seated. As the starter motor draws a lot of current a poor connection would allow the electrics to operate (poorly) but the starter motor would struggle to operate - this fits with your symptoms. Here's a vid showing an example. In this case a hair line crack in a fuse - the fuse looked ok and metered out ok, but with the engine running it was like a little on/off switch! Jump to the 30 sec mark to see the problem.