Last year I found both lychee AND rambutan at my Sam's Club, and this area is by no means well-populated or culturally significant, being in Arkansas. I was quite surprised, and they tasted good. You may have luck at there or a Costco. I was really surprised, doubly so when they had rambutan...
I'm growing a container longan (3 actually though graft died on one so its future grafting stock now probably for a lychee variety as well) for a similar reason. I figure that I can't get these fruits most of the time anyway, so If I'm able to get a small crop, it's probably still about as much or more as I would have to pay for yearly...
However, missing from this discussion is the fact that you can actually induce flowering in longan and lychee with chlorate, right? This is what I have been wondering: how well does this work on containerized trees, and how much does this stress the tree? How much does this fact help us in the real world? Would this have any realistic benefit for either of us growing outside their natural zones in more artificial situations?
Reading this got me thinking - why are folks like you and I here? I mean, don't you have a mature fruiting lychee tree growing? And you still need to plead for the fruit? This tells me that all of the effort I'm putting into grow these potted trees in my backyard might not produce the amount of fruits I want, if any at all
IMO Once you start growing out of zone like this generally the value of the fruit is negligible to the value/utility of the tree and raw plant material (scion wood etc) in most situations. (And even if you don't get fruit, you have a "backup," a "genetic record" to graft onto something or plant in the future). Even with figs some people make way more money with the trees than the fruit itself, and figs are top tier to begin with.