You're taking the right approach to getting all the crap out. Just keep hitting it with water until you can get it to flush clear. At least it's summer lol
I flushed my 99 Suburban with Simple Green. I drained as much as I could of the old coolant, poured in 2/3 of a gallon of Simple Green, topped off with clean water.
If you haven't had any more oil getting into the system and you're pretty sure it's not mixing into your engine and trans oil, then give it a shot.
You shouldn't leave Simple Green in there for long, but it wouldn't hurt to take it for a drive and give it a little WOT. These degreasers aren't easy on Aluminum (your rad and heater core) but having it in there for only an hour or two isn't going to hurt anything.
The Simple Green will also help wash out any leftover oil residue.