I didn't read every word in every post, but I did scan them.
As I read in the early posts in this thread, this is for road equipment, where the OP can't predict until arrival whether the thing the equipment will plug into has a balanced input or a single-ended input. The OP doesn't know how the equipment is wired beforehand.
So, don't do this with cables. That has been written already.
One of the most respected devices for this purpose, which is well known in pro audio for this exact use case, is the Henry Engineering Matchbox HD.
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This active device will amplify the negative side and provide a 6-dB gain going from unbalanced to balanced, and will address the standard noise issues going from balanced outputs to an unbalanced input. It does not use transformers, but rather an arrangement of op-amps, and thus it introduces negligible noise, particularly in a live-sound environment.
Rick "has a couple of these, plus a home-built device that uses similar THAT specialty op-amps for making this conversion" Denney