Need to do a lot of short sleeve transfers - what kind of press?

Hi all,
I have a 500 piece order to do individual vinyl names on short sleeve gildan 2000 navy shirts next month, in addition to a 2 color screen print front. I'll cut the names out on my Graphtec CE6000-60, but need to find a good way to quickly heat press them on.

Would a hat press work? The ones I see don't seem to have a good way to fit the short sleeve on, but I could be mistaken.

I've also looked at the DK8 tag press, but don't know if you can get the sleeve threaded easily.

Any suggestions for quick heat transferring on the short sleeve?

Thanks!