Answering my own question here in case it helps anyone in the future.
Bitfocus Companion needs to be used to get this to work. The commands must be set to tcp-udp instead of internal. Change the command end character (in Companion) to CRLF - \r\n (Common Windows). In order to fire off Trio macros from Stream Deck, you'll need to hit the macro on the keyboard, then call up the Commands window to see what the actual command is that was fired off. Copy that command and paste it into the Command area of Companion.
We weren't able to get the deck talking to Trio without going through Companion.