You can definitely make an argument that some rooms simply will not accommodate FRFRs/PA speakers for practicing and that is particularly true if you are crammed into a small/tiny room. Excellent advice regarding treating the room and doing the best you can to get good sound in whatever practice space you have available with your existing monitors. However, the OP was talking specifically about taking presets designed at home to the stage. Proper acoustic treatment of the room and moving to preset design on monitors that more closely resemble what you will be using on stage, are not mutually exclusive.
I maintain that the more closely the monitors you use are to resembling PA speakers and whatever you will be using for FOH and to monitor yourself on stage, generally speaking, the more seamless using the same presets for both environments (home, stage) will be. This is similar to how using an FRFR on stage with your modeler can often be a better predictor of what the FOH will sound like. This is the approach I prefer. Many users have experienced this when using studio monitors or headphones at home, only to arrive at rehearsal or the gig and discover that the presets they created at home, which sounded so brilliant, don't sound even remotely as good on the stage. There are no absolute rules though. Some users have no problems on stage with the presets they created through headphones or studio monitors. So, if that works for you, go for it.
Also, probably preaching to the choir here, although true that we often mistake louder for better, there is a qualitative, not just quantitative, difference between different volume levels - Fletcher-Munson. The sound may not be intrinsically better at higher volume, but it is perceived differently. That is the primary reason you so often see the advice to make sure you have vetted your presets at volumes closer to performance levels before using them at a show.
The OP was specifically trying to address how to most easily ensure that presets designed at home will transition seamlessly or at least with minimal tweaking to stage. For me that is using FRFR(s) for preset design with final tweaking at closer to performance volumes. Using headphones or studio monitors is not IMHO the straightest path to accomplishing that goal, YMMV.
I totally agree that presets should have a final dial in at volume, however IMO it is a fallacy to state that FRFR should, or needs, to be used.
FRFR is a marketing hype term without any specification, and those specs that ARE offered typically have slack tolerance vs those same specs of studio monitors. Also, every FRFR sounds different, some have unpleasant artifacts but again, at the end of the day they are SUPPOSED to represent EXACTLY what studio monitors are .. a faithful, amplified reproduction of the source. There are also cheap FRFR as there are cheap studio monitors, there are expensive FRFR as there are expensive studio monitors. There are bassy, bloomy, bright, peaky FRFR just like there are studio monitors.
Buying new monitors, or an FRFR is not an instant solution to improving the matching of presets created to tracking at volume on stage through some random PA. and, just like you would "dial in" the EQ of the room/PA you should also "dial in" your own monitors & room.
Essentially, what is important, just like in mixing with monitors with known unpleasant artifacts (say
cough NS10), is to KNOW what they SHOULD sound like, and luckily, every single user is given a master template to check their system in the form of the AXEiii factory presets. Play those at volume, and add parametric EQ, or OUTEQ to make those sound tonally balanced .. problem very much largely solved imo.
Essentially, If you play a known amp in the factory presets and ended up adjusting the amp to reduce low mid hump, adding more low cut, tame highs etc etc.. then you need to know its your SYSTEM, not the preset!.. and your preset will sound thin and bright everywhere else. In reality, just know that the factory presets do not just sound good, they can sound unbelievably awesome..
I would very much recommend, learned the hard way, to reserve OUT1 for the PA, connect your monitor/FRFR/speaker setup to OUT2, have OUT2 copy OUT1 and use OUT2 EQ to make those Factory presets sound tonally balanced... without adjusting the amp in the preset and you are done. At this point you have somewhat normalized your system to that used to create the presets and setup a profile for your system..
This would strongly suggest that any presets you create will be reasonably true to your hearing of the Factory presets, and that using OUT1 for the PA gives the sound guy a solid, but blank canvas to tweak to taste, or if that guy is you, you can setup an OUT1 EQ for that system/room venue.