How long would it take to run the extra Chester-Crewe-Airport service via Gresty Lane and the independent lines then fast to Wilmslow now?Correct, platform 6 is the only one with access to both the Chester and Manchester lines at Crewe. What's an even bigger problem is the fact you'd need find another two windows to cross the WCML on the flat every hour. Either reason alone would probably be a deal breaker, but the two together.....
The extra Chester train is needed to get away from the current 20/40 minute intervals, a fast airport service could use platforms 11 or 12, it would certainly improve access by rail from the SW (and might be as quick as the current stopper,) and if 769s were used it would reduce diesel running a bit more.
The Chester services currently arrive in Crewe at about xx.20 and the slow airport trains leave at xx.16, so allowing for a traction change-over and the reversing move they could be fairly close arriving at the airport if that one was sent, but if an extra Chester train arrived around xx.40 then went to the airport it might work...