From Skyscraper City.... here's my suggested route in from the south. Three assumptions made:
1. Lichfield to Wilmslow is dealt with easily, plenty of space, so not worried about this piece.
2. Terminate at Mayfield/Piccadilly (take yer pick)
3. Airport Interchange Required.
Its going to be easier to see it Outbound, North to South - and white is above ground (cutting/embankment/bridge as required), orange is tunnel.
Leaving Terminus head south alongside or taking over two lines of the 6 track viaduct as far as Longsight Depot, drop off viaduct in green space and into a tunnel.
A mixture of tunnel and above ground where possible through Levenshulme, Burnage and Heaton Mersey - not too many properties lost
Tunnel under East Disdsbury and proceed above ground down to Mersey, bridging it and the M60
..and the M56, skirting between Gatley and Benchill, using a small tunnel where required (could just demolish a dozen houses instead)
Then its above ground in the green strip between Wythenshawe and Heald Green alongside Styal Road
Until it cross the Airport Railway Spur - the perfect location for an Airport Stop (via an integrated shuttle service up and down existing railway link) - this would sit above the spur and MAELR Western Extenstion - some houses on Ringway Road would have to go. HS2 continues south from here towards Styal
Squeezing between Quarry Bank Mill and Styal Village before entering a tunnel as it approaches Wilmslow...
Finally emerging to the East of the WCML and bridging over the A34 and continuing South Easterly above ground towards Lichfield
Thats only a total of about 3.5 miles of tunnel - considerably less than what is required to get out of London.
Just my view. Comments?