As a sanity check regarding journey times, the
Disused Stations website has an extract from a 1922 Bradshaw timetable for the Peak line.
An express took 1h25 from Manchester Central to Derby Midland non-stop, or 1h30 with one stop at Millers Dale. A stopper took up to 2h50, depending on how many stations it skipped. The Midland route from Central via Cheadle Heath to Chinley was a bit longer than today's routes from Piccadilly, but less congested.
There were few direct trains from Buxton to Matlock. The Buxton branch was mainly served by a shuttle from Millers Dale. Buxton to Matlock journey time was 1h on a direct train, 1h5 changing at Millers Dale.
AIUI the Hope Valley Capacity Scheme only provides paths for 3tp2h of freight, the same as today. The additional capacity is for passenger trains.
I think unused freight paths are a bit of a red herring. Freight traffic flows are inevitably variable, because they have to flex to match customer demand. But if there are insufficient paths to meet the peak demand, that flow will be lost to the railway. Each train can carry 2200t of aggregate. If one of the three paths is removed, that can mean up to 80 more heavy lorries needed per 2 hour cycle, or a lorry every 90 seconds on the A6 or A623!
The capacity crunch might come in the 2030s, with NPR wanting a 4th hourly fast service through the Hope Valley, on top of the 3tph provided by the Capacity Scheme, and HS2 wanting paths for 2tph through Chesterfield and the Sheaf Valley, in addition to the services from Nottingham and Derby.