I'd say a variation on the Edale Skyline but adding in a few more up & downs would be good. Doing the skyline anti-clockwise take as many right hand downhill variations as you can. I like dropping off right into the valley after Lose Hill, then climb back up to Hollins Cross, drop-down to the bottom of the broken road and climb up the side of Mam Tor following a track on the southern side near the crags). Follow the normal route but when you get to the top of Chapel Gate drop-back down to Dale Head / Nether Booth in to the valley rather than along Brown Knoll. From here you can go up Jacob's / Crowden or Grindslow.

The thing with 3 peaks is that the hills are after a long, fast flat run, each peak being an attrition on the last.