Hi R and all,
If you make a better antenna than your antenna you have a serious problem! I see "I connected an RG-6 cable directly to the driven element." in another post. (No need to put driven in quotes.) That tells me it's a dipole insulated from the boom which is about 75 ohms so using RG-6 you have a perfect match. The trouble seems to be an imbalance, OK on HF but disastrous on such a high frequency. Like Gary said a balun is the key or at least should be but there is a major problem, it's ratio. A TV balun WOULD work if the feedpoint impedance were 300 ohms because it's 4:1 which matches down to 75 ohms but it's 75 ohms to begin with! 50 ohm coax would match up to 200 ohms but that's NG too, what you need is a 1:1 balun but they just don't make one for 800MHz, you'll have to wind one yourself and for the hobbyist that's usually a dead end.
Hey, INSPIRATION! I just realized what's inside a two way splitter, a 1:1 BALUN! Think about it, it's 75 ohms input with two 75 ohm outputs but each is unbalanced. The key is each is 180 degrees out of phase with the other which provides a push-pull or balanced output except for the ground which BTW isn't connected. Unless I'm barking up the wrong tree, open the case and remove the guts, set aside and attack the case with a hacksaw. Leave enough to mount it VERY close to the element so the leads remain short and don't become part of the element and you have the F connector for the coax. Then wire it up, being exposed it won't matter in the attic where weather won't get at it. Remember, lead length is super critical at these frequencies, what you add you must subtract from the element so try not to add any.
One final note, if you must you can run the coax down the axis of the boom and end mount the antenna. That way it won't detune the antenna and won't cause pattern distortion, to the signal it just looks like part of the boom.
Good luck, if at first you don't succeed at least we'll find out how far you can throw it. (;->)
This paragraph is a left-over from a previous edit but I'll leave it even though it's out of place, it may come in handy if the home made balun doesn't work.
Now go back to the drawing board and come up with a continuous element mounted to the boom without an insulator and a gamma match. This design is used in single channel UHF TV antennas and works fine with RG-6U coax. By this time you're ready to go out and buy an 800MHz Yagi or plug yourself in since you make such a good antenna. (;->)