Nice problem ..........
I'd start with a big map, pins and some cotton.
Stick a pin in each county town.
This will give you a good visual of where each one is.
Then wrap a length of cotton between all the pins.
Measure the length and try a different order of pin.
It's a quick visual method of getting at least a first approximation of a route.
Plus you cannot miss a town by mistake.
If I was doing a closed loop .....
I'd probably start in the east where it's flatter, so I could cycle myself fitter before the hilly parts.
I'd also try to avoid the scottish highlands in midge season .....