Doe the cafe have a compost bin for their customers like Whole Foods does? They have a trash bin marked "COMPOST -- food wastes and paper napkins go here".
Another way to incorporate the paper products into your kitchen waste is to use them as the liner for your in-kitchen waste container. I use a paper grocery bag inside a plastic grocery bag and put down paper egg cartons and/or pressed pulp fast food beverage tray in the bottom to soak up extra fluids and to create some airspace in the bottom.
When I take this out to the compost pile, I just turn over the plastic bag and slide the whole thing out. (I repurpose the dirty plastic bag for general trash collecting so I don't feel bad about not recycling it). By this time, the moisture has started to break down the paper bag and pulp products (I tried paper bag without the plastic bag to keep it drier, but if I don't get around to taking it out before the moisture soaked through, the paper could rip and cause an abysmal mess.) I can control the moisture level of the compost piles by adding more water if necessary.
If the outside container needs to be tightly closed without aeration for sanitation reasons, etc. You might consider incorporating Bokashi composting in the holding bin. I think it can be relatively inexpensive even after buying the EM if you make your own Bokashi, especially in the larger quantities you probably need. Adding the Bokashi microbes will enable you to compost things that are not always considered compostable. EM can help to keep down the smell too -- it's used to spray down cowsheds and pig pens. It has it's own distinct smell that some people don't like, but I think it smells like some fermented pickles like sauerkraut and kimchee.
I think it's great that you are doing this, and it's important to try to figure out the best way so you can succeed. I can imagine that maggots and flies are anathema around food/restaurant establishments.
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