There is some good stuff left or right of the chew ressy.
Long drag up the chew road but all rideable. To the left you can do chew and long which is a reasonable techy route with 3-4 options for a descent back to dovestones and to the right you will eventually get to Alphin which is one of the best descents in the areas or if you peel off before Alphin you will pick up the secret sausage which will drop you out towards Tintwistle/Stalybridge way. The first bit is a bog fest but after that is an awesome singletrack…..follow the stakes!!!
if we have had some heavy rain I would give these routes a miss I went up that last trail you mention, exploring [no one do this, go down it], and that is some serious bog on the top. Go up there in winter and you might not come back.
To the OP – the climb up to Alphin via Buckton quarry is a good one. Not on the OS map, but it’s easy navigation on the ground and a nice pull to the top. Decent effort but no hard gradients. You then have the choice of dropping all the way back down on a fine descent, or traversing across to Chew.
Pennine way over Black hill looks to be a good way of making some loops up there – must be busy with walkers though at the weekend? I know people are less up tight at the Peak top end compared to Edale etc, but the Pennine way must be one of the busier routes.