Ok, I'm going to jump in on this one.
You've got good designs, a good company, but no means to produce the designs on the shirts.
You've got experience putting together events and getting sponsors.
You've got connections to the local music scene.
Create an event. Get sponsors. Get paid. Take the profit and print your shirts.
If it sounds simple, that's because it is.

Especially with the experience you say you have.
Here's an example:
Last year we put on a comedy show in an upscale venue. One of my good friends is a comedian and hooked me up with some well known comics, and I had Damon Williams headline the event.
We gave away tickets on the radio, and promoted it like crazy. Radio, flyers, posters.
Let me run down the tab for the event.
Radio every day for 2 weeks-$1500
Flyers and street team-$500
Venue rental-$3500
Comedian's travel and performance fees (3 comedians plus host)-$7000
How much we paid out of our pockets-$0
Sponsors!!!
We got all kinds of sponsors that contributed for everything. Space on the flyers, banners at the event, getting mentioned on stage, space on the program.
We sold out a 600 seat venue with ticket prices of $20 & $50, and didn't have to pay a dime for any of it.
On top of all of that, we named the event after ourselves.
We also had some local rappers that were pretty well known perform after the show.
So, maybe you could put together some kind of concert. You've got the connections. You've got experience getting sponsorship dollars.
Put your know-how to good use! Come up with some kind of event people will like. And have fun!