I would contact the dye manufacturer. I'm sure they can offer suggestions that will help.Sadly, no. Not if it's like my washer. If I want to lift the lid I have to press the button and sometimes it will drain before it unlocks the door :/. If I guess the right time during the soak cycle I can catch it with water, but normally no. These washers that think they're smarter than us are annoying. I think there will be a backlash and people will start demanding the old dumb washers.
I don't know how one could go about dyeing clothes in a new washer. I'd probably do the soaking in a bucket and then dump the whole thing in the washer to drain and finish up.