So the simple solution is to eliminate all of the free parking and replace it with paid parking and loading zones. And raise the price high enough so that there's always spots free close enough to where you're going so that vehicles have a place to park themselves for short periods of time that's outside of the travel and bike lanes.
There's free parking in Midtown?
Yes there is. We've just zoned it for streetside parking.
I live on 26th Street. We have a bike lane, a traffic lane, and two sides of street side parking. This is the case across a large faction of Manhattan, the avenues exempted. For Exhibit A in stupid parking lanes, I present Broadway.
Just pull up satellite imagery on Google Maps and it'll all be obvious.
You see the sea of red lines? Those are all places you cannot park.
The best way to make delivery drop-off points available is to get rid of all the free parking and make it all paid, and keep raising prices on a block-by-block basis until there's typically spots free on any given block. It'll be a minor marginal cost for someone making a delivery to pay, say, $5/30 minutes (this will probably actually be cheaper if it means they can find a nearby spot, thus saving time driving around and time shuttling things from a farther spot). But $5/30 minutes works out to $240/day, which will easily discourage long-term parkers who shouldn't be using the scarce resource of on-street parking in busy areas anyway.
In less busy (i.e. purely residential) areas, it might make sense to move to a permit model, with permits costing several hundred dollars per month. There'd of course be parking meters mixed in with all that for people who are driving to the area and don't have permits.