This is why I get so annoyed by the "Reopen Woodhead" brigade. Although it wasn't originally on Beeching's hitlist, one of the factors behind its closure to passengers in 1970 was an inability to find a way to divert services into Sheffield Midland. There were other reasons behind it, of course, like political pressure to keep the Hope Valley open, but this was a major practical problem that couldn't be solved. If Woodhead had been the only rail route from Manchester to Sheffield, you'd have been dumped at the remote and inconvenient Victoria station, with no other onward rail connections, and it would have caused a lot of issues. If Woodhead were to re-open, you'd still have the same problem now - you'd need to provide a diversion into Midland across a densely populated and highly developed area. If it was too difficult to contemplate in the sixties, I can't see it being much easier now.
Having had a look, short of major construction work in Sheffield city centre, I think you'd have had to take trains off Woodhead at Penistone and run them via Barnsley. It would have made the journey somewhat longer, and required the expense of electrifying that section.