On to your situation. In home composting is always tricky. My wife and I do indoor/outdoor because we have a yard. In your situation, I'd advise against vermicomposting for the same reasons you listed. I was the technical manager for an enterprise vermicompost startup. Our facility was a rowhouse basement and the owner of the property was a founder. Flies are unavoidable, as is the occasional vermischwitz. They are fragile guys and minor mistakes have major consequences. The exact ratios escape me, but 1lb of healthy, mature red wigglers can consume half a pound of Green (fresh) cellulose in a day or two. We were engineering soil additive, so we supplemented heavily with Gray (dead) cellulose (cardboard, paper, etc.) In an attempt to hit profitable output. I will spare you the further details of our failure. Suffice to say that vermiculture is tricky in the best circumstances.
My suggestion to you is twofold: use the Bokashi Method (https://www.planetnatural.com/composting-101/indoor-composti...) and find a friend with a garden to offload your Bokashi Tea. That link is one of the first hits on Google (read: not vetted) because if you go this route you are going to be reading a lot and there are many roads to Rome.
This is very short due to medium, but if you'd like to discuss in depth and at length I'd be more than happy to. Both composting and waste neutralization are passions of mine. Just let me know how to contact you should you desire.