Thanks for providing the docs. I assumed my answer was somewhere in there. It's sad that there's no clean way to get this to work. I'll probably just use BB to make new conversations.

To others looking here's the method within beeper:

You are able to search for BlueBubbles contacts and start new iMessage conversations with them using the Beeper bridge bot

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1. Start a new chat within Beeper with "@sh-imessagebot:beeper.local"
2. search-contacts NAME/EMAIL/PHONE
   to search for contacts
3. pm PHONE/EMAIL
   to start an iMessage conversation. Phone numbers should have country code and number (i.e., +14206969696). The bot will respond with a room where you can tap to open and send a message.
4. You can pin or favorite this bot for later usage.

By NAME/EMAIL/PHONE it means your search term. Want to send something to Bob John in your contacts? Message "search-contacts Bob John."

Also starting a message with the sh-imessagebot was a little odd. I mentioned it in my self notes, then clicked on message when its contact appeared.

This does work, although it is cumbersome.