I have just re-read this thread from the beginning to get some ideas.

Could the handbrake be stuck partially on?? The hand brake is much more efficient when rolling backwards, so would stop you then, but only slow you down going forwards.
Could also explain the poor gas mileage??
A quick feel around the inside centre of the rear discs after a few miles of driving would pick up any residual heat.
Be careful - it might be real hot.

Winter switch - IIRC I read somewhere that the winter switch only works if the temperature is under a certain reading. This was to stop people using it when not needed, as starting from a standstill in 3rd gear is never good for the transmission.

Ok - now I will duck down and let the real experts tell me how wrong I am.
It's always fun.

PK