@AnswerInfinity a few questions...
Did the rest of your monitor mix sound like it was latency free and was your sound arriving late in everyone else's monitor mix?
Did the whole FOH mix sound like it was arriving late when you moved over to listen to it or was it just your channel on the desk that sounded late in the FOH mix?
What was the venue's FOH speaker configuration? Any delayed speakers at the back or was it just one set of speakers at the front? Seems very strange to have a delayed FOH signal for the FOH speakers right by the stage. Any audience clips from the night we can hear? Usually if the whole mix is arriving late to the crowd, you can hear the acoustic drums on the stage followed by the "slapback" of the delayed mix.
I'm assuming you've tested your presets after the gig with and without the extender box from the night and found that there isn't any latency in the Axe as expected. What was the extender box you used?
It would be worth troubleshooting more and sending the engineer from the night a friendly message asking what the desk was and if they still have their show file with your band's mix from the night saved. If it's an X32 or M32 we can easily load the show file and see if there was any time delay being added to your channel or anything else. As an FOH engineer i would be more than happy to do that as it's always worth solving problems for future shows.
Not sure why folks are suggesting that a limiter would add latency to your signal. Limiters tend to be applied only to the main FOH sound system if there are any noise restrictions, but they don't add latency. Some engineers might compress their whole monitor mixes but that's not a very good idea. Individual channels would probably be compressed. Regardless, if there was any limiting being applied to your Axe (a stupid idea given that your modelled amp tone is already compressed in the preamp modelling), you would hear it clamp down on the sound when changing presets from quiet to louder patches.
I wonder if the engineer applied a short milisecond delay as an insert on your channel, thinking it would thicken the sound up, but set it 100% wet.
+ 1 for future gigs to use either IEMs or a power amp and cab. I can safely say as both a musician and FOH engineer that using house monitors for amp modellers isn't a good idea. Every monitor wedge will already have some heavy eq on it, specifically with some typical cuts in the lower and upper mid frequencies which are the most important for any guitar sound. So already your tone is being compromised by going through the house monitors. Running a power amp and cab is a must if you're not using IEMs. Or, if you're not singing any vocals, ask the engineer to run your wedge totally flat without anything added.