A question about ham antenna baluns?

I am running 100 watts (max) out of an old kenwood. I run 50 ohm RG-58/U from the transceiver to the antenna. The antenna is a G5RV Jr. dipole, it is mounted in a horizontal inverted-V pattern in my backyard up at about 25 feet. Because the G5RV Jr. is pre-made it has already hooked up to it, about 20 feet of some balanced line (it has a twin-lead style and doesnt appear to be a ladder line type of feedline) After the 20 feet this terminates into a (female) SO-239 plug. That is where i plug the unbalanced RG-58/U coax into the connection. I put up a 1:1 choke balun to help keep common mode currents at bay but obviously my SWR is HORRIBLE! I am running the internal antenna tuner (to keep the SWR from destroying my transceiver) in the kenwood and because of the high SWR i never run over 50 watts (even at 50 its a bad idea). Now despite all the reflected power i have been able to make some contacts (im in Machusetts and was able to hit new Hampshire, new jeresey and georgia) but those might be flukes! without a doubt i need to bring down my SWR, so my question is what should i do? should i put a step up balun in place of the choke balun? if so, what impedance step up is needed? (2:1, 4:1, etc).......so what should i do? i dont want to run the transceiver until i get this fixed