Just what we all absolutely adore, an intermittent fault !
But bear with us, moff, it looks like we may be (at last) making progress...
I am now almost certain that the black alchemy that is "RF interference" lies at the heart of your problem, rather than any fault in your G50 system.
As I indicated earlier, there's almost certainly no way that connecting cables can, of themselves, actually cause this type of problem, however, if I'm right, they'll have almost definitely added to the "witchcraft like" variability you've experienced.
I'll now try to explain (as clearly as I can) the theory that's behind both my earlier question and my current "Aha !". (Be warned: this could get messy.)
The key words are "Yes, the G50 receiver is generally on the floor with the rest of my pedals..." and also your saying that (it) "...appeared to be triggered by my position onstage, which may indicate environmental interference or proximity to my amp as I moved back, or to the pedalboard as I moved forward."
Well spotted and well described.
Now, in 99.99% of cases, there will be no problems whatsoever with a Line 6 Relay receiver operating in (or on) a device-populated, floor-sitting pedalboard exactly as you have done.
(Congratulations! You are the lucky one in ten thousand to have been chosen for this special prize, ...without so much as a single "click here".)
Although higher positioning of the receiver is always recommended, (for "accidental stomp" reasons, as much as for obtaining a better line of sight from the beltpack to aid reception) Line 6's data stream is nearly always robust enough to cope with nearly any configuration.
So I'm suggesting that the problem is not related to your beltpack's RF, but rather one caused by the induction into your system of "junk" radiated from another floor-bound device, or even a weirdly unique combination and correlation of such radiated "junk" from several (or all) of them.
(Effects pedal LFOs and BFOs are prime suspects.)
In terms of radiated RF, your (I'm guessing, superbly fit, ...in common with all Line 6 users) body acts as a large capacitor, conspiring to create a gigantic "tuned circuit" when it's fine form acts in concert with any (or every) nearby connecting cable. Each of those cables also has the innate ability to act as a reflector and/or an inductor and/or an antenna when placed in that kind of RF "circuit".
Hence the unpredictability. (The opportunity offered for stray radiation to enter your G50 receiver via the plastic components of its housing may also be a factor.)
Now for (what I'm hoping will be) "the cure"...
I'm presuming that you run something like a 5m (or 15ft) jack cable from the last device in your pedal-board's "daisy chain" to your amp input.
What I'm now suggesting you try is to
Relocate the receiver to sit behind you, on top of your amp or amp head, with just a short additional lead being now required to connect from its output to your amp's input,
Effectively "reverse" your long lead to now take your G50 receiver's output down to the input of your pedal rig ...and
Then use Line 6's supplied wall-wart from a power board behind your amp, as the new location would otherwise force a longer cable to clutter your performance space, should you stay with your former powering arrangement.
The thing about all radiation (be it RF "junk", sound, or light) is that it follows the Inverse Square Law. Double the distance and you don't receive half, you receive a quarter - the "inverse square" of 2.
Conversely, bring your source of radiated "junk" four times nearer ...and you'll swamp your circuitry with sixteen times as much of it.