A couple of comments for the OP; If you are running balanced transmission line, you will need a BalUn at the antenna end, for one reason, you are feeding an unbalanced antenna, but also, I'm guessing your feed point is ground level, and your transmission line is going to enter the antenna system in the same plane as your counterpoise system, and as a consequence, the fields and reflections presented to your transmission line, will present themselves from the radiator and the counterpoise, un-evenly, to the balanced transmission line, unlike they would in a center-fed dipole, where the matching "problem" is evenly presented to the balanced transmission line, (since a dipole, whether horizontal, vertical, or inverted V, typically has the transmission line enter the antenna's structure, symmetrically between the two radiators) and can be contained very well back to your tuner. So with that in mind, you should put your BalUn, 1 wavelength from the antenna feedpoint, and run coax from there.
The other question is why is your antenna non-resonant? Is it because you are using it for multiple bands? Or did you build a 5/8 wave without adding any inductance? If you posted your antenna dimensions, and limitations (like how long/tall the structure you're using to support it), you might find others here could help you optimize your design.
