Tom's 'quiet' route out of Carlisle is recommended and the bit down beside Southwaite is much preferable to the A6 on the other side of the valley.
And I would disagree with ESL's dislike of the A65 - I dislike the dual carriageway bit south of Kendal; it was too scary when I last rode it and I found the slip roads/signage confusing coming north, but I was extremely tired.
I liked the Endmoor/A65 alternative but I'm guessing Mr ESL has much more frequent use of these roads than I.
For finding Burton Services, I'm sure the wee lane is signed "Cinder Barrow Picnic Sign" (a brown tourist sign), then left near the top and over a cattle grid toward the heavenly lights of the services. One remembers these things when it's an inky black night and one is exceedingly tired and narked off.