They are very deep tap-root trees. It is not recommended to ever move them. You should however be able to find a few this year seedlings which might be movable.

I have a couple of named ones which seem to be slow growers too, but every year plant a few more seed from the largest ones I can get from my friend, these seem to grow faster, but I figure 3-5 more years till I get to see fruit.

George

They're very different from most temperate deciduous trees(well, they are the sole surviving temperate zone genus of a group of 'tropical' plants), in that they carry out virtually no root growth or activity during the dormant season.
Root suckers do not transplant with very high survival rates, but if you're going to attempt to do so, a late summer(August)move is best; with an early spring move, just as they're coming out of dormancy, a close second. Same time frame holds for seedlings - if you could ascertain that the shoot you were digging was indeed a seedling, rather than a root sucker.