Only other thing I could think of would be a systemic, but I am extremely leery of systemics in fruit you're going to eat.

Remy: Thompson seedless are naturally small berries. What you are seeing is somewhere near the normal berry size of that cultivar. Commercial growers achieve larger berries by spraying gibberellic acid to first thin the fruit off each cluster and then to plump up the remaining berries. They also use other tricks like girdling the trunk. You could do this. It's not that hard. But it doesn't increase the flavor or sweetness and may do the opposite. Doing a better job of pruning, thinning, and other cultural tasks can increase berry size somewhat if they are limiting factors. Commercially berry size increase is used only for Thompsons destined for table grape use or other special applications like Jumbo raisins. The normal raisins are grown with small berries just like yours. So the vast majority of Thompsons are grown like yours with small berries.

I'm new to this forum, and I do want to thank Myardor, fruitnut, harleysilo, and others here for the info, pics, and suggestions. One reason I come to forums like this instead of trying Google first is that Google usually gives me tons of extraneous information and links to sites that aren't all that relevant and/or are mainly commercial advertising sites. Usually, if I can ask a question of someone who's knowledgeable in a field, it's a lot more efficient than just searching through the library's card catalogue or wading through all the stuff that Google yields. However, if I ask a question in a forum, I don't expect people to go out and do my library or google research FOR me if they don't already have the info. :) I just see forums as places for people to share info and opinions and experiences they already have - or to direct each other to good info sources. Speaking of "pruning," :O back in May I had a guy doing some yard work for me and he was totally incapable of following instructions or directions. Long story short, after we had carefully moved all the long offshoots from my 22-year-old purple Concord grapevine onto the trellis I wanted to train them to, he proceeded to take a chain saw to the 5-inch diameter main trunk of the vine, right near the ground! (No, I didn't kill him, but I wanted to!) The stump hemorrhaged sap for at least 2 to 3 weeks. I tried grafting some shoots from another (Champagne) grape onto the stump, but I don't think that "took" because it was too late in the season. Anway, new growth has been sprouting from the old stump ever since late June, and the leaves look very healthy. Does anyone how long I'm likely to have to wait for a decent crop of grapes from this severely "pruned" old grapevine?

Unless your ground is frozen, plant them outside now. They will arrive as bare root pruned plants, but if the ground is a little warm, they will set root this fall. I hope you didn't order a bunch of seedless grapes. It should be illegal to sell them in the East without an explanation that they need to be sprayed from July til harvest. At any rate, plant the grapes where your arbor is/will be. Pruning in the early years is important too.