Water will mix with trans fluid and make it look like a milk shake. Then it must be flushed.
If you made metal shrapnel in the trans from your trans destruction method, the metal mess will be in the converter, which is bad for the bearings. Plus it will get into the pump.
Get a rebuilt or flushed converter for your rebuilt trans. Also flush the trans lines and trans cooler in the radiator of abrasive debris, or it might make your new trans fail.
It sounds like you may have removed most of the harmful contamination and should hopefully be ok. Keep and eye on the fluid to change colors after first using it. Like Robert said, converter was likely not helped by the burnouts, but should be ok.
My guess would be that the water did not hurt it as long as you flushed it out like you said you did. I don't know if the converter is ok after your grass burnout episode but if reverse works it gives me hope that the converter still works. The converter does not know if the car is going forward or backwards so it appears it is working.
Your trans is wiped out. Go to a transmission shop.
