The Arcane Bore from Thaumcraft can also do sick touch if either the focus or the pick have the enchantment. It has no problem with being moved by frames, although you'll probably want to rig some way of autoplacing a vis relay every eight blocks it moves so it can run faster and repair the pick as it goes.
I recommend aiming the bore sideways to the direction your frame machines moves, so it digs out a very wide (or deep, if you aim it downward) tunnel. You'll need some other sort of block breaker on the front, of course, for that to work, but that's not hard to do. You'll also want to swap out the pickaxe every now and then to repair it (note: if the pick has the repair enchant, the bore won't use up the last point of durability), which can be done with an enderchest and an EnderIO item conduit attached to the arcane bore block itself (the swively thing, NOT the base).
My testing indicates that it takes almost about 58 seconds for a bore with Potency V on the focus and Repair II and Efficiency V on a Pickaxe of the Core to mine out 5 x 40ish blocks after being moved sideways. I'd like to have it move when it's actually finished mining out a layer, but I couldn't figure out a way to do that, and it worked pretty well on a timer, as long as the bore doesn't stop moving for some reason. If you opt for silk touch on the focus instead of the last level of potency, it'll run a bit slower, but not too much slower. You could, of course, put Silk Touch on the pick instead and not sacrifice speed, but that's probably more difficult, even with Thaumic Tinkerer's Osmotic Enchanter (which is bugged in the version packaged with Infinity 1.0.0 and 1.0.1, if not the more recent versions- you'll need to update TT to make the enchanter not crash your world), if you want to make several picks to swap out periodically.
Finally, the only automatable way I've found to recharge pickaxes with Repair is to put them in another Arcane Bore that's being supplied with vis from an energized node. Once again, EnderIO is capable of pulling damaged picks out of an enderchest, putting them in the bores, and pulling them back out when they've repaired themselves. Just note that it will try to put the picks in the focus slot if you don't put something else there- an unupgraded excavation focus will do. Also, I recommend building this sort of setup outside, with the bores facing the sky. They won't try to mine anything if you don't give them a redstone signal, but... better safe than sorry.
You might be able to use RF-powered picks, which would be much easier to recharge. I haven't tested it, though.
