There is a cheat (I’ve thought about trying it myself). Start at Bakewell, Monsal Trail South to Haddon Hall, Bridleway to Rowsley. A naughty bit on a concessionary footpath from the Grouse and Claret to Peak Rail at Rowsley South, steam train to Matlock, East Midland Trains Matlock to Duffield, Ecclesbourne Valley Railway Duffield to Wirksworth. Then High Peak Trail to past Hurdlow, over to Monsal Trail at Blackwell Mill then South to Bakewell