Cody ... while I don't fish rivers, or from shore (nowadays) ... casting a jig upcurrent of a bridge piling, either alone or under a float ... or fishing the eddy water spots ... would be some tactics I'd use, if faced with that situation.
And, I must commend you on your floating jighead/tail hooked minnow tactic That's using the old noggin !! I've been known to use a similar rigging ... slip sinker/floating jighead ... when fishing from shore on some small lakes.
... cp