I’ve done it (Manchester to Sheffield on road there, off road back for charity) but I don’t have GPX.
There is surprisingly very little road if you work it properly and from Stockport to very near Sheffield it’s really good mountain biking. If it helps at all, you could maybe stitch together:
Follow River Mersey and then River Goyt to Woodbank Park, Otterspool, Chadkirk Chapel, Marple, Roman Lakes, Mellor Cross, Birch Vale, Hayfield, South Head, Rushup Edge, Mam Tor, Edale, Jaggers Clough, Win Hill, Bamford, Stanage and Fox Houses. That is in reverese of our route and I don’t know the names of the Sheffield areas but I remember we rode through a large park near the city centre.
It’s a tough old mtb ride.