Personally, I couldn't bring myself to put soap on a Tony Miller or SRD, or even a Kanayama, but too each his own. That's what's good about a forum like this, you can find out all kinds of info. If I want more draw, I have latigo, if I want less, I have horsehide. Funny thing, The soap works because of Tallow, and maybe the lanolin?
Tallow is animal based, if it's the real deal, now, Neetsfoot oil and mink oil (the real stuff) are rendered animal fat too...Same thing? Kinda/Sorta? I think if I had a strop that needed conditioning, I'd go the neetsfoot route. I don't think I'd rub my strops down with soap, just to do it. There'd have to be a good reason. I have about 12 strops, and I really like them the way they are. YMMV. I have one strop (not mentioning any names) that I'd experiment on.