To answer original question… looking at the block diagram for the GLD-80, it does appear that you are insert a source (“Ext IN”) directly into a matrix. According to the diagram, this can be a local input, input from the I/O card, or an FX rack. Unfortunately it doesn’t appear that you can insert a group or buss however. Therefore, if you have several audience mics that you want to push through to the broadcast mix, you might need to use a FX rack. Combine all of the desired audience mics in a single FX send going to an FX rack, and then choose a FX that can be “transparent” and not actually have the FX turned on. It sounds like you can take the output of this FX rack (which isn’t doing anything) and insert it into the matrix.
Now for an unsolicited explanation on how our church handles our broadcast mix. Like you, our church does not have a dedicated broadcast mixer" and effectively have an “unmanaged” broadcast mix. Here is how we handle it…
First, you don’t want to use the L/R mix as your foundation for the broadcast mix. The sound in the room is going to be different than what is needed for the broadcast because of the ambient audio in the room that isn’t present in the broadcast mix. Therefore you’ll definitely get better results when you can dial in a broadcast mix with different send levels than what FOH is doing.
This is how our church does this. Set up a dedicated Aux for the broadcast mix (which sounds like how you handle it currently). However you want to set this up as a “Post Fader” mix which is counter intuitive from most of the advice you’ll see about setting up a broadcast mix. You should add the audience mics into this aux just like any other source.
During rehearsal, the FOH engineer should dial in the FOH mix to their liking and then switch over to the broadcast mix to dial in the mix there using the broadcast mix send levels (mixing while having selected the broadcast mix buss). Ideally this is done on a per song level and saved as a scene (ie song 1, song 2, etc), but it can be set once for the entire service (although your results won’t be as consistent song to song this way). But by dialing the FOH mix first, and then switching over to the broadcast mix, you can effectively set the foundational levels between inputs on the broadcast mix to achieve a “good mix”.
Then the FOH engineer goes back to mixing FOH as normal (ie stops mixing on the broadcast faders). However now any changes made to the FOH mix will also be made on the broadcast mix too. If they need to push up the guitar during a solo for example, it will be changed on both mixes. If there is a quiet piano only song and the FOH engineer needs to bring down the vocals to match (or bring up the piano) then these changes are made on both mixes, etc, etc, etc.
While this solution isn’t as good as using a dedicated broadcast mixer, it is MUCH better than trying to use the same L/R mix that is being heard in the room as your foundation for the broadcast.