There are places that have smallish companies operating as a food delivery intermediary (e.g. mosi.ch claims to employ 100 deliverers -- likely many of them part time). I would expect such companies to be somewhat close to the range of models you are considering, so I expect them to have stumbled into many of the issues that I wouldn't even imagine that would arise.
I would be afraid of running into some unsolvable tradeoffs between privacy of customers and ability to detect some kinds of antisocial behaviour from various parties (e.g. how would we deal with areas that no deliverer wishes to serve for whatever reason? if we consider that fine (or consider much higher delivery prices there fine), this is IMO too close to extremely laissez faire capitalism to net the benefits I think you expect. the only ways to prevent that that I can see rely on social pressure, which requires some transparency into delivery orders accepted/rejects).