Yes the tone stack is close to a Fender TMB with a few added switches and components that form the Mid-Shift and Deep circuits.
My perception is the Mid-Shift changes the upper knee of the bass control. If the Bass control is fully CCW (off) the switch has no effect on tone, regardless of the position of the Middle control. In one position the Bass control mainly boosts low frequencies. Change the Mid-Shift switch to the other position, and the Bass control reaches up into the mids.
The Bright switch does exactly what the name suggests. Essentially a small capacitor is switched in to bypass more highs around the Gain control. Capacitors block lows and pass high frequencies. As you turn the Gain up, you may notice the Bright switch has less effect. The V-Type is fairly bright preamp, so you may never use the Bright switch.
The Deep switch is actually a fairly wide and deep mid-scoop.
I don't know where nominal flat is, but my guess is around 4-8-1. I think of it as clock positions, so Bass between 9-10, Middle between 2-3, Treble off or almost off. Of course the setting for nominal flat depends on which position all of the toggles are in.
I do not have the owner manual for the hybrids, but I will attach the OM for the original all-tube V-Type, which shares the exact same preamp circuit.
Yes you should be able to get some drive if you really crank up the gain. However, IMHO this preamp really excels more at clean. But definitely try it and see what happens.