Despite the myths (and some here will disagree with me), the large flavor molecules in brines do not penetrate into meats more than a milimeter or two at the surface. This is not the same with the salt, which will slowly migrate throughout the body of the cut.
Marinades can add flavor, but it is again a surface treatment, mostly from the marinade literally sticking to the surface of the meat. Mops are the same idea.
As you have mentioned, you can inject a liquid into the meat, and then it is inside, but it will not penetrate past where it is injected.
Therefore, your best plan, depending on what the star ingredient you must use is, is to find a way to get it more intensely applied to the surface of the meat.
Depending on what you have, this may be to:
- Incorporate it into your dry rub
- Incorporate it into your mop; for liquids, possibly reducing it first (for example, an ale) to intensify the flavor without the bulk from the liquid
- Reduce it and inject it, knowing that the flavor will pretty much stay where it is injected
- Rules permitting, incorporate it into your sauce (again, possibly reducing it for intensity)
The more bulk of the substance you can get to adhere to the meat, or inject into the meat, through these methods, the more powerful the affect will be.
Since taste is closely related to aroma, I would suggest sticking to exterior treatments such as rubs and mops, where the aroma will trigger the taste perception more directly.