When I was at Art College we made ink for etching by mixing pigment powder with oil. We put a small pile of the powder on a smooth slab and made a pit in the middle, then we poured oil into the middle and gradually mixed it into the powder with a scraper until we got the constituency we wanted. Sometimes we would add a hint of another colour to the black so that where it ran thin it had a shade such as green, brown or blue depending on the look we wanted.
If you went to an art supplier you would get printing ink powder, or as I said - use henna powder to mix with the oil.
I think drying it will be the problem as it will not behave like either water based ink or Plastisol. You might have to mix it with alcohol or similar to get a base that you can print but which will then flare off when you heat it. You'll also have to experiment on the best kind of screen emulsion (or paint your own screens). Try a few tests with what you have in the house before you go to any great lengths. Buy olive oil and henna powder and try that - you could do that today. Let it sit for an hour after mixing and then mix again. Paint it on to bits of 100% cotton. After printing make sure you wash it. Maybe the pigment will stay in and the oil will wash out?? Maybe someone else can comment on how best to dry it. You are definitely onto something original here. I can imagine a fuzzy natural look that might look good with the right designs.