Time to disrupt the notion of 'delivery': Sign up to drop off a package or two and get access to the internal city streets for x hours. What could go wrong?
Package-carrying bikes can take a surprising amount. https://www.carvelo.ch/de/private/modelle/data/51.php
Anything that can be carried by a bicycle courier, must be. Anything else, <6am or >9pm (for example).