Most on-street parking isn't paid, so almost everywhere that's green on that map isn't available for delivery services anyway; it's going to be taken by personal vehicles that move twice a week for street-sweeping. Add more on-street parking and you'll just have more people with personal vehicles using it; it won't make it available for deliveries.
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.
