Being the curious sort (and a Prime customer), and a little annoyed I couldn't remember the specifics, I ordered a $12 adapter from Amazon. Anyway, it worked fine in the Joey that previously had the Dish Bluetooth adapter.
I also plugged both into my notebook, and as I suspected, both were Broadcom BCM20702 based, but the one from Amazon reports as just BCM20702 and the Dish one reports as BCM20702A0. The hardware IDs were different, too - the Amazon one was USB\VID_0A5C&PID_21E8&REV_0112 and the Dish one was USB\VID_215A&PID_2001&REV_0112.
Both work fine in the Joey, but the Dish one will not load a driver in my notebook (actually I tried it on 3 very different ThinkPads with 3 different OS's - Win7, 8.1 and 10).
My guess is that most anything based on that Broadcom chipset might work in the Joey, though.