I think ericb2400 is getting really close to your problems. Your cultivator and hillers are so close to mine that I checked my tractor to make sure it wasn't missing.
Do you have other trailing shank arms like the ones on the wheel sweeps? You need to have a trailing sweep/furrower behind your hiller discs. You can reverse that arm and reverse the foot on the bottom to make it work if you don't have other shank arms.
The wheel sweeps can be on any type of shank arm and could be mounted on two forward arms if you have them. That would allow you to use one of those shank arms for the middle furrow. Getting the wheel sweeps in the dirt at an angle will help to pull the cultivator frame down and make your hiller discs dig in more. Loosen your feet and drop those wheel sweeps down to the about 1" of shaft above the foot. Adjust your toplink for the best digging characteristics. Make sure both left and right sweeps are set exactly the same depth. If your cultivator doesn't have downforce, the hiller discs just roll along and lift the whole cultivator instead of throwing a good hill.
Also, your hiller discs need to be about 6" closer together and maybe angled a bit more to throw more dirt. Bigger diameter discs can be further apart and throw more dirt for a bigger hill. Your discs look like 12" or 14". The problem you will run into is that sometimes the A-frame for the 3PH has bolts that interfere with just where you want to place the disk shank arms. You could drop those hiller disc down a bit more. I know you don't seem to have my clearance when transporting the cultivator, but that's just the nature of this type of setup and your lift arm geometry. I carry mine just a few inches off the ground with the 3PH all the way up. If you go over rough terrain, you may have the plow digging in.
I can't tell you much about your soil except adding sand and mulch will help break up that clay. Unfortunately, it takes a lot of sand to make a difference. I pick up soil and squeeze it into a ball in my hand. If it sticks together in a tight ball and any moisture squeezes out, it is too wet to plow. If it crumbles easily when you release your hand pressure, it will plow well. If it is malleable, it will clump, but if it is crumbly, you can get it to fluff up by repeated tilling. Tilling also really speeds the drying process.
I am sure that sandy soil grows the best potatoes, but clay soil will surprise you with how well it grows some crops. Okra seems to love clay soil and so do peas and beans. Any plant similar to melons that likes to develop extensive roots and use a lot of water to form fruit will do better in sandy soil. Potatoes will probably do okay, but they won't form as pretty as they would in sandy soil.