Without trying to be offensive, it sounds to me like you're talking in circles. You keep mentioning the balance is "upset" but don't offer the reason why, other than the balance is upset.
If the
5000 ohm choke is right at the coax tap point at each end so there is no unchoked coax to radiate on either end, then there's no evident reason why the balanced line would see more than a negligible unbalanced current path at either end to cause it to go unbalanced and radiate.
I'm going to build and try it and I'll report back when I do later in the Spring if not sooner, win or lose.
I have to admit, I'm cheating a little since I already know it works, there's 360
yards of 450 ohm fed this way at a dx cabin I've been to which replaced LMR400 because of too much loss to the 10m beam on top of the hill (1200w of 1500w power
loss) but I wasn't the one who built and matched that line, and I want to try it for myself.
I want to see how hard it is to find the 50 ohm tap point at each end and if it moves or changes once the other end is tapped.
I'll be using 300 ohm TV twin lead (because I have 500' of it!) with 100w and will see what amount of loss there is by reading how much wattage is present at the other end of 500'.
I'll find a park and lay out the 300 ohm in a big elevated triangle so the antenna end is close enough to me to read the watt meter, unless I can get someone to go with me in which case I'll just lay it out straight. I have another Gainmaster I'll probably use on a 6' pipe hammered into the ground.
I'll also walk the 500' of twin lead with a field strength meter to check for feed line radiation.