I think most of the mines are in the same general region down there, but the pike mine is closed to both business and public. Apparently, there are piece of stock just literally on the surface, but taking such things is obviously discouraged.
I am not aware of anything else, no matter how close, that is the same as a washita. A good mid density soft stone may be close, and a bad soft stone is just junk. Dan's softs are very fine stones for a soft, but they don't stay active long. Nortons, I just haven't had enough exposure because ...well, they have the washitas (but like I said, the later ones of those aren't that great (the ones that say "washita oilstone" on the sides, and they bring a fair bit of coin sometimes).
Having tried what I've tried, I'd say that the non-Dan's softs (natural whetstone's version being my favorite) feel like a stone made of grit particles, and washita feel like a matrix with holes in it instead. As you've found, some of the softs can be quite gritty and fast.
I mentioned natural whetstone's "hard", which is really more like a soft ark - it's also a good stone, but the same issue remains - they never get as fine cutting as a washita stone, and when they get fine, they get really slow. Washitas generally retain some cutting.
As far as oil, anything thin to thicker works fine on a washita. The thicker oil will maybe help a little bit with fineness, but not that much. It will also suspend whatever you're sharpening away from the stone if you're sharpening a flat area like a chisel back. It just depends on what you're trying to do. I have seen oxidized oil allowed to settle into a thick layer on the surface of a stone in a strop top box (being used to sharpen razors), and I'm guessing that was done to slow the stone down and make it cut more finely than it actually is. I don't like that, but someone found it workable. (I have sharpened razors on washita stones themselves and as long as one has a good linen, the edge turns out fine. That's not the case with any of the various soft arkansas stones).
So, in short. The white soft arkansas stones from natural whetstones are my favorite soft stones. I'd avoid dan's softs (dan's has the absolute best fine black stones I've ever seen, vintage or new, and their translucent stones are also as good as anything that's ever been mined, but their prices are getting very high and seconds are hard to come by). I've only got a few stones from Natural Whetstone company, so there's no guarantee they're still the same, and for anything else, it's really difficult to say - it depends on who mined the stone and what they have. The difference in speed and fineness with a cheap gray and pink thin stone that I got as a soft from one maker and dans is probably a factor of four. natural whetstone is in the middle. None of them ever quite match a washita, and it's easy to see why they were offered at half the price of a washita in old stone catalogs.