Delivery Bike

Well, you could try doing both but then you would have a problem
fitting it on more than one dimension of bike, ie one bike's specific
head tube angle and size. My problem with my rack isn't how it's secured,
it's the gap between the rack and my bars.

Agreed. If the parts that "lock" the fixture into the frame are adjustable (on slotted holes, for example), it could be made to fit different angles/geometries.