For decades, a friend grew in swampy areas. He'd float 30 gallon peat pots inside inner tubes with the bottom few inches in the water. He'd tie them off to the willows, all around.
If moisture is sufficient but the water shallow enough, you could use the same pots, or smart pots to take advantage of the moisture.
Think about this:
Use the large peat pots but fill them only far enough so the bottom of the plant's root ball barely reaches moisture, and the plant is fully exposed.
As the plant grows, remove the lower leaves(not stems) and apply rooting gel before further filling the pot with soil.
You can do this several times as the plant grows, adding a few inches at a time, insuring the plant gets water while maximizing its root mass.
Always saturate any soil you add to insure good contact with the plant stems, to aid root development.
Even though the plants are getting moisture from below, drench the soil, any time you visit your garden.