Okay so I took the plunge and tried using my HE Washer. I used only a single yard of fabric since I wasn't sure how this was going to turn out.
After doing the initial dyeing in my buckets I used the cold water from the bathtub for the initial rinse. The water was still colored when I put the fabric into the washer with some synthropol and some detergent. I set it on hot and let it do it's thing. After it was finished just to be safe I ran it through with nothing but water, one more time.
it looks like it did a good job on the fabric, I've tested for running and the excess dye all seems to be gone. I am going to run the washer through now with a piece of white fabric to see if I have any excess dye, but it looks like it's fine.
So just as a disclaimer, I'm not recommending you do anything that is outside your comfort zone. I chose to try this (I have an LG frontloading washer). If you choose to it's at your own risk!