Unless you have quantities (and time) to justify the "pre-sewn" route, why have you ruled out transfers?
In my mind, the only reason would be that there is a specific hat you wish, and it is a six panel with a seam in the front. Five panel hats are not as plentiful, but there are some out there.
There are folks who churn out nice, quality, detailed plastisol transfers all day long, for either light or dark substrates.
Your idea of printed patches then sewn on is even more labor intensive than a standard transfer, unless the look and feel of a "patch" is what you or they specifically want.