I think it would be good for you to try a few of the Direct to Garment printing fulfillment companies yourself, that way you could see FIRST HAND which of them has the quality you prefer.
There aren't any minimum orders. You can just upload your design and buy one and have it shipped to you.
Try out CafePress for yourself, try out zazzle, try out printfection, try out Spreadshirt's
DTG (not the flex printing which was rejected because it would take too long to weed)
You may find one of them fits your needs well.
With the small gaps in the design, you may have a hard time of getting the design to look EXACTLY the way you want to just because of the nature of ink on cotton. It's not like pixels on a screen that stay put, or ink on a paper. Ink on fabric spreads. So while some fine lines can be done, you will still have some
dot gain.