Do you have your verb set for spillover? Maybe the abrupt change is causing a noticable gap? If the triaxis is switching too fast you might want to map your effects to not change presets unless you have to. I used to use a Boss SE70 with my triaxis which was a great for effects but had very sluggish processor when it came to changing presets. What I had to do was basically set my Verb' to taste and map the presets to stay on one preset and use a CC if i wanted to turn on a delay or any other effect (which was rare). I would put the SE70 in the loop so I could use the Loop on/off as a bypass. I later bought a mixer but had phasing issues so i decided not to keep that effects setup (but it was great to have 2 half rack pieces and the potential to keep the tone in tact).
Is this something you are noticing only when playing alone or with a group? Personnally, I have not used my Triaxis much with a group, but I would keep it on a single sound usually. My mark IV has seen more use with a group but then again I really don't do much switching with that either. So, suffice to say, i am nowhere near an authority on how the Triaxis behaves with a group utilizing the switching functions. At home it switches fine to my ears (with the exception of LD1 Red which exhibits some rambunctious behaviour sometimes but what else is the redheaded step child of the triaxis expected to do? Be good? Yeah right!). At home I am using a very simple processor which I am not entirely sold on (digitech gsp1101) but it works for the time being with its verb, chorus, and delay being the most practical effects for me.
There are a few ways around this:
Use your volume on the guitar (which you seem to already be doing)
Use a boost pedal over a clean channel for your rhythms
Use a CC pedal to drop the gain, change the tone, and raise the master instead of changing presets (this will probably be great for a subtle change over a long period of time but seems like it would just be overkill in practice)
Have a nice spillover on your effects processor so the channel switching is not an abrupt silence or set your effects processor to stay on the same preset if yours doesn't do spillover
I might be way off base or maybe you're just used to switching delays associated with most multichannel amp designs, but hopefully you get some ideas to deal with it.
Greg