I think that might solve the issue quickly.
Saint Jim, patron saint of on-street parking.
You are subsidizing private enterprise by tolerating organized violation of traffic laws.
If you want delivery companies to be allowed to behave this way, then make a law. It's perfectly reasonable for a municipality to except certified delivery companies from some traffic rules...
An actual workable solution would be to simply not allow deliveries to a building unless it has an available commercial delivery spot. That may make some businesses unhappy however. Residents may be unhappy to see entire sections of the city suddenly have no walkup businesses as well.
Point is, you can change prices, stop offering the service, or fix the law.
But allowing businesses to ignore the law is not a good idea. Change the law instead, if that's what you want.
Interesting. Over here, a company cannot deduct parking tickets (or similar payments). They are not cost of business and are therefore directly reducing the EBIT i.e. money of shareholders. Also, they are treated as taxable income to the person who got the ticket, if identifiable (here enforcement is weaker, but the outcome is that no company pays parking tickets for its employees.)
If the cost were increased enough (perhaps by enforcing the law more aggressively), UPS might choose a different strategy such as telling its drivers to park legally and walk further.