Dan, you were fortunate enough at Swinderby to have several runways from which to fly, so the crosswind issue was less of a problem. As a student I flew Chippies at White Waltham and again, plenty of runways and even better, all were grass.
At RAF Abingdon even with 2 runways at right angles, there were days when the Bulldogs could fly, but the Piston Engined Agressor Squadron AEF cowboys were grounded.
Flying with the left hand didn't seem to present any difficulties to our students when I was QFI-ing.
When the MoD flogged off the Chippies, it was suggested that I should acquire one for the station flying club. Much to my regret, I refused - we only had one RW and I was also pretty sure that someone would probably overstress, someone else would over-rev and quite a few would probably groundloop as there was only one RW.... A Chippie is fine as a privately-owned aeroplane looked after by doting owners familiar with the breed, but too much of a risk for a club owned aeroplane. We also considered a Bulldog - until we thought about the maintenance costs and fuel burn.
But both the Chipmunk and Bulldog were infinitely better military trainers than the T-67 or das Teutor!