I have 2 DTG (direct to garment) printers. They are MUCH better quality than screen printed (washability is the same) but these print photo quality graphics directly (screen printing cannot compare) onto the shirt- there is no transfers involved. They are big, though, and cost about $15k each so I am not sure if I would like to bring one to the show. But if we took preorders, like when people register, I could print them befoehand and have them ready for folks when they arrive at the show.
Or, I could print out the shirts with everything except the name, then at the show, we could print out their name on a transfer and just press it onto the shirt in the name space. I have a press and printer we could use to print and press at the show...
Just some thoughts...