Re. Tamping down the layers - I've seen use of a hydraulic tamper in rammed earth construction. Hydraulic tampers mostly are terrible for human joints, but I did see one design to get around that by making it taller and heavier with the part that the operator holds onto on a sort of elasticated sheath, to reduce the joint strain. Also, if or where the walls are wide enough for it to not continually slide off and be a pain to lift back up, how about one of those lawnmower shaped tamping machines?
Re. Mixing the material - again in rammed earth construction I've seen that done with a small bobcat type of digger. Of course it depends on scale, location, hire costs etc., but that's probably less expensive than a concrete mixing truck and you don't have to add too much water to get the mix moving.
Feedback from those with hands on experience? Thanks!