Potatoes also need oxygen to the roots for good tuber formation. You won't get potatoes growing deep in the middle of that pile. I would suggest breaking into rows maybe 16 inches wide and maybe a foot tall, one the plants are growing you can add a bit to the height if you want, but keep the root system not too far from the outside surface of the row to allow enough oxygen penetration into the soil.
As for direct planting into a mulch material, I have seen it work, though I agree it is much more likely to get waterlogged. I usually go with a decent soil for the potato and then add some compost on top of that. Then I keep adding as they grow.
In Iceland and whatnot it was common to grow potatoes in old hay and they went nuts, but the hay was not that broken down and did not water log to quite the extent that will. If you were going a less rotted hay I think that giant pile method work great. With the slightly rotted hay and mix you have there i would suggest the potatoes have a "layer of soil to be in with this material above it. You could even throw some of this material on the ground in rows and then throw 4 inches of soil on top of it and put in the potatoes. Throw another four inches soil over the potatoes and then throw more of this mulch on top of that. Keep building the mulch up over the top of the rows as the plants grow out. This will hold in plenty of moisture to help the plants have a steady supply.
One of the biggest issues with potatoes are uneven amounts of water supply, too much at one time and then not enough and then back to too much is problematic. Slightly too much everyday not actually as problematic, or not quite enough throughout the entirety of the season not quite as problematic. One advantage to using the mulch there is that it will hold water like a sponge, but it could also increase the likely hood of rot problems. I always make sure to put my potatoes directly into soil even if it is like this year just an 8 inch thick layer of soil between layers of mulches.
I laid down a layer of mulch, covered with a bit of clay from a hillside, then some forest floor soil over that. Then I covered the potatoes with more forest floor soil and then a layer of needles and forest floor duff. I made my rows a bit wider than normal but I am going with drip irrigation this year and I wanted less rows to plumb reducing cost.
I would have gone with less cover at the moment but we are still getting down into the teens and low 20's at night and still getting a fair bit of snow, so I covered my rows pretty good with mulch to protect from too loww a temperatures. As the plants get about 10 inches tall or so I will add more mulch to those rows until they are about 18 inches tall or so in the center.