It's starting to sound interesting now what with veiled suggestions that it's not possible. 😉
I reckon from the lower Barn, using the fastest route (which may include a fair amount of road from the barn to Peel tower) there and back, the *three* towers is possible in less than three hours by a fast rider. Possibly much less.
Something like. Barn… cane it over to Bolton and thence to Ramsbottom, up the long cobbled road, peel tower. over the top to Entwistle, witton weavers to Darwen moor and the tower (although it may be quicker to roll down into Darwen and then up the crazy road climb). STraight off the front and then road to Belmont. Up the Belmont road climb, georges lane, pike, down through the woods to the barn. BAM!
Cross bike would do the job nicely.