The remap is just to address the stalling, and looks to have corrected the accelerator pump mapping (the burst of fuel when you twist the throttle). I experimented with a PCV accelerator pump and could reproduce the stalling issue, and I measured the A/F and performance on the dyno immediately after the new tune was installed and it made no difference to power or A/F in any other area of the RPM/load range.
This means it makes no difference to whether you have an x-pipe installed or not, so do it in any order you like.
The adaption process is done when they remap it, as the Triumph software let's them apply it instantly. It only effects idle though, so most of the claims of "my bike runs so much better now" are probably placebo, but if it makes people happy...
Well, of all the Thruxton's we've run on the dyno I have never seen one that ever runs lean under any situation other than over-run (when the injectors are almost turned off). There is a wealth of contradicting evidence about this out there, but we have the latest DynoJet system with a brand-new dual A/F sensor, and it tells us that the bikes run rich at all times except idle and cruise (when the O2 sensors lock the mixture to 14.7:1). Dyno gas analysers will indicate lean if the intake is partially blocked, there is an air-leak, the wide-band sensor is contaminated, the bike has SAI (ours doesn't), or even if the sensor is more than a couple of years old. They will pretty much never indicate over-rich unless the bike really is rich.
This is one reason I don't suggest people use a BoosterPlug, as it's simply intended to richen fuelling, which is great on a bike with no O2 sensors that runs slightly lean, but on our bikes it will still be 14.7:1 at idle and cruise, and simply over-rich under acceleration.