I have never used any special kind of overdrive for my rotary sound - I just use the same overdrive that I use on my guitar, always putting the rotary before the amp and adjusting the amp gain using my guitar volume knob in conjunction with a pedal volume pedal. I also never use any of the overdrive pedals in the FX3 because I think the amps always sound better. The amps I gravitate to for overdrive are Bassguy59, 5F8 Tweed, Class A 30W, Brit JM45 Jump, and ODS 100 HRM. Each of these does something different for me and it seems like I am never happy unless I have these 6 available to choose from for a particular "dirty genre"... I will also mention that, unless I am recording direct, I turn the power amp simulations off for all patches since I use a Mesa Boogie 2:50 tube power amp live (which is ironic since I originally bought an an AxeFXII to get rid of tubes in my life!). And also no speaker simulation (unless recording direct) as I am already going through a nice amp cab in real life. As far as tweaking the rotary block in the FXIII, I pretty much use it as it is already set except I think I adjusted the default high speed a touch faster (and depending on the application, I use a wide range of mix settings - from 100% for that thick rotary "fill the room" sound we associate with this effect, to 30% or less when I am using it as a chorus effect)
I will also followup on my original post on rotary pedals: Before settling on the Ventilator II, I had tried (and returned) all the major rotary pedals including Leslie, Boss, Lex (was good), Rototron, RotoSim, Mini Vent II, Soul Vibe, and I think a couple more I cant remember now... Some I returned immediately, others I would use a few months before selling off. And FOR ME, the Axe rotary was hands down the best for feel and sound - giving me a tone option that extended my playing instead of limiting. When I was playing in my blues/fusion trio, I used it a lot - probably going to it for at least some period on a least a third of tunes - sometimes for solos and heads, but more often for adding an extra dimension while comping for the bass player's solos or to simulate the sound of a B3 comping. That said, it may be that FOR YOU, you need the sound of the Ventilator II to give you that unconscious feeling of identity that you want - which is why Fractal has always included an FX loop.
Oh - and I will just add that the new iteration of virtual capo is REALLY good! If you are trying to get a B3 tone, try mixing in a bit of virtual capo at -7 half steps into your tone (one of the primary tone bars from a B3) This was not available to me when I had my trio...