Whilst beloved of wargamers the Chi-Rho symbol was not in fact much used by the "later Romans" at all - if you look through the Notitia's western shield patters you will see exactly zero use it for example. The possible/probable use of it by Constantine is just documented for 1 battle as I recall.
As far as I am aware the LBMS ones for the post-Roman Brits is not based on anything either other than, maybe, Arthurian mythology.
Personally I have gone with Notitia patterns for my Roman(ised) units in that period on the basis that there could have been continuity but equally you could use pretty much any Roman-Germanic iconography mash-up as equally plausible IMO. There are good arguments that the army that the Gallic Foederate army represents was just a Frankish army anyway ...