My calculations came in at 3720 miles. If I include Anglesey and Skye as they are connected by bridges the total goes up to 3925. Even allowing for errors, that's a lot of miles.
This won't be a rush job as we will want to see places as we travel so I've provisionally planned to do 125 miles per day. That's 31.4 days.
With fuel consumption of 25mpg it's going to take 157 gallons which won't be cheap, about £860 assuming £1.20 per litre. Add on B&B for 30 days and food along the way and I think I'm going to need to win this competition!!
Roll on the sixteenth when I find out if I've made the final 15 to go to a vote.