The Woodhead axis is not relevant to modern needs though, not pointing directly at anywhere on the East end and requiring long and difficult approach lines.
If you are going large it needs to be on the Sheffield - Stockport axis, but even that is really tricky - if it’s a really long base tunnel then where do the East portals go?
Well the woodhead axis does have the advantage at the east end that it is on the north side of sheffield, it is a potentially usable Manchester-Leeds route as well as a Manchester-Sheffield route.
The southern route is better at the western end, but mainly, I think, for access to the airport and thus the HS2 alignment into the centre, assuming it is built obviously.
EDIT:
Whilst you will not be able to fill a line with solely Manchester-Leeds traffic, you could probably get close to filling one with all the Manchester-Leeds and MAnchester-Sheffield traffic.
Could be operated by 140-150mph bi-modes.
Probably wouldn't be a traditional "base" tunnel due to the relatively minor peak altitude and gradients, the tunnel is just to reduce public opposition and impacts in the Pennines.
So you could use a single tunnel bore inside the valley wall, with flat/near-flat adits every 1000m for escape purposes. Large sized TBMs that can do the job exist now.
You only need an escape bore for a few kilometres in the middle.