I think you'd best beware of anyone who says they're not "guessing" (as I am) with regard to this strange artefact, Geoff...
My only thought would be to try an experiment that involves "rolling off" the top end response of your XD-V handheld by "muffling" its input with additional foam over its metal windscreen, ...by which I mean layers of something like the non-acoustic "furniture" or "light bulb" packing foam that's denser than that of popper-stopper windscreens.
What I'm getting at is the "speed" with which each mic handles transients, setting aside (for the moment, ...but nevertheless remembering) the fact that the Line 6 XD-V handheld presents an electronic, digitally-created frequency response "model" of a beta58 as opposed to the purely passive electrical signals that come from Shure's original.
As it happens, I'm blessed in that my old ears regularly benefit from true "state of the art" monitoring from the multinational likes of A.T.C, Dynaudio, Focal, Genelec, Neumann and/or my trusted Sennheiser HD25 headsets ...and those old ears tell me that nearly all of Line 6's "models" seem a bit "faster" in handling top-end transients (in vocal mic terms, above roughly 5kHz) than the "original" cabled dynamic vocal mics upon which they're based.
Same when an original Shure beta58 PGX wireless "head" replaces Line 6's capsule atop an XD-V handheld.
Hence the proposed "trial" that I'd like to hear about.
Should my suggested rough and ready "removal" of some of that top-end spectrum diminish your "ghosted" artefact, it would be a "pointer" to the way that TC Helicon's VoiceLive Play unit actually "handles" a transient response that is faster than that from the cabled mics for which it was originally designed.
(Sadly, I haven't one here that I can try as the acquaintance that owns one is currently overseas with hers.)
"Is there something I'm doing wrong or is this just a situation I'm going to have to live with..."
I reckon you'll already have discovered that there's not a lot you can actually do "wrong" with either device !
(That's one of the main reasons I love both of them.)
As for living with it, I'm wondering how evident your "accidental chorus" would really be over a system at an actual gig, as distinct from a direct "A to B" comparison in the "splendid isolation" of the home or rehearsal "studio" ?
Your thanks are very much appreciated, Geoff, ...but I'm sure you appreciate that being in a position to occasionally "repay" the great assistance others gave me is both a privilege and a reward in itself.
I doubt, however, that I've been much help at all with this particular problem...