It's difficult to transplant just about anything that's growing in sand, except prickly pear. If it is really sandy, the soil will fall off the
root, so you will be doing a bare root planting. I would do it in the winter when the plum tree is dormant. Plant it quickly after digging it up, and keep the
roots moist until you get it back in the ground. Don't let the soil dry out real bad, but you don't want to waterlog it either. Mulch it with leaves and
water it occasionally and it
should be okay. If you transplant
enough trees, your odds of having a few survive will increase. There may be a way of getting cuttings and rooting them in water first, but I'm not familiar with that. I'm sure someone on this forum would know. Best of luck!