Bi-amping can have some benefits, but I think it’d be wise to spend some time getting familiar with the charms of your new tube amp first. Maybe do some tube rolling and find a tone you love, then later on experiment with bi-amping. Some tube amps with the right tubes can have some fairly dynamic bass. Tubes amps sometimes get a bad rap for flabby bass due to low damping factor, but some can have kick ass bass....its much less of an issue with lighter weight woofers and amps with stout transformers. There are several factors involved. Even my lowly Dyna/VTA amps have tight dynamic bass with 8" kevlar woofers in a T-line...they’d likely struggle to drive a heavy 15" woofer. CAT amps just kick ass with any woofer. So try your ARC with your SFs, experirment a bit, and see what you get first.
What you’re considering is known as horizontal bi-amping (using a different amp for bass, and another for mids/highs). There is also vertical bi-amping when two identical stereo amps are used...one for each side with the separation benefits of monoblocks, but with two channels per side. One channel for woofer, one for mids/highs. I use my two Dyna/VTA 70s in a vertical bi-amp mode, but I do add a powered sub from 40hz down to augment the lowest octave, powered from the tube amps speaker outputs to the high level inputs of the sub. It works well if I keep the gain of the sub down.
Both vertical and horizontal bi-amping can have pros and cons, and can be done using passive or active crossovers. I’m assuming your SF speakers have separate inputs?