Hello MakePlayoffItsFrusteratingDohK,
Thanks for reaching out to the Apple Support Community. I know how important it is to be able to depend on your messages working as expected. With the outgoing message being stuck as you've described, it may help to sign out of iMessage entirely, then restart and sign back in. This will ensure your connection to the iMessage server is fresh and solid.
To sign out you can navigate to Settings > Messages > Send & Receive.
Tap on your Apple ID to select "Sign out", then restart your phone as normal. After the phone restarts sign back in by going to Settings > Messages> Send & Receive and then click on 'Use your Apple ID for iMessage', and be sure that "Send as SMS" is turned on again. That should clear the frozen message and allow you to re-test.
If you run into any trouble or have any questions, please let us know, the whole community is here to help.
-Best Regards-