You don't mention the Korg models but am assuming that they are not Kronos keyboards. Anything less than a Kronos will probably not yield a good organ result from a Korg synthesizers. The Ferrofish is probably a step up but in my view still not satisfying (but I'm a Hammond purist). It kinda depends on your budget from a module perspective. I use a Voce V5+ with a Neo Ventilator and also use a Hammond XM2/XMc2 also with a Neo Ventilator. Other choices might be a Nord Electro 2 rack, but you will need a drawbar controller as well as the new HOAX HX3, which sounds absolutely fabulous but also you'll need a drawbar unit which is just now coming out. Looking at about $1100 for the new Hoax and drawbar unit but guarantee you will have no issues with how it sounds. It depends on how good you want your hammond/leslie sound; the better you want the sound (as well as drawbar control) the more it is going to cost.
Hammond XM2/XMc2 (has a built in leslie, not the greatest but passable) (discontinued but still expensive, probably $1K)
Voce V5+ w/ a Ventilator (Voce is a hammond only unit, no leslie) (around $750).
Ferrofish B4000+ (step up from where you are, not satisfying enough (for me)) $400.
Nord Electro 2 rack (dated, but certainly still usable) Hard to find, probably $850 is a good price
HOAX HX3 (The distributor is Diversi and in Morton, Pa, not too far from you) will need a drawbar controller to go with it. $1100 for both
VST plug in's (VB3). sounds fantastic. Under $100. Will need to run from a laptop computer/IPAD.
Also, putting this in google "ferrofish youtube" will bring up several B4000+ videos. If you think that these sound good enough to you, then I think you have your answer. The issue is that the B4000+ is not very popular, if you didn't like it you might get stuck with it unless you were drop the price to a point where someone would buy it. I'm with you though, I didn't want another keyboard for hammond, which is why I went the organ module route.