Well, the Leeds idea suggests a triangluar diagram similar to the one that currently works my regular train home, the 14:50 from Aberdeen. Suggest Leeds (06:00) -> Inverness (13:00) -> London (22:00 or so) -> Leeds. A corresponding working would be Leeds (06:00) -> London (09:00) -> Inverness (18:00) -> Leeds. Thing is, that leaves you with three services rather than two. The alternatives would be two round trips from sets based at Bounds Green, or co-operation with Scotrail so that the first morning working from Edinburgh, the 08:34, could be used as a positioning move for a Craigentinny set to work south to King's Cross later (it arrives at 12:03, so 13:00 is possible) and eventually head back with an early Edinburgh train the next day (say the 06:00). Going the other way, the last Edinburgh train would come back on say an 08:00 to Inverness and return with the last day train, the 18:44. It requires Scotrail to sub-lease the set for part of the day, but might be helpful since they would still get a big cut of the settlement.