We used to do the trench method before decrepitude set in. We tried dropping the chitted seeds onto the surface, then covering with black weed fabric - still let some light through, so needed a thicker cover. Then we started using a Mantis (after a full sized rotavator), to chop up the manure finely, but I still crawl along the rows planting into the soft soil with a trowel. The results are very good, but by the end my knees are screaming, so I wouldn't want to plant the number you do that way.
We used to have a rotavator which had a potato planting attachment, which opened up a trench, you dropped in the spuds, then closed it up afterwards. It claimed to earth them up as they grew, but we never used that. Somewhere you must be able to get something similar.
If not, all I can think of is to borrow a couple of kids, with the promise that they can do the magical bit of digging them back up when ready - unearthing spuds is one of the wonders of gardening.