Triode or Ultralinear mode

What you are missing is an amp that is designed to operate solely as a triode amp.  I've had two amps, a Cary and a VAC that offered switched operation and both sounded rolled off and dynamically dead in triode.  My BAT VK 55 is pure triode and is the antithesis of the other two.  It is dynamic with a pure sound that ultra linear can't quite match.
So in your case, stick with ultra linear.

"My BAT VK 55 is pure triode and is the antithesis of the other two.  It is dynamic with a pure sound that ultra linear can't quite match.
So in your case, stick with ultra linear."

rhljazz- Is your assessment with the exact setup, but different amps? I would think there are amps that offer UL/triode  switching, and don't kill sonics as you describe? I don't know if your BAT operates in Class A, or if its like the others which are A/B? Maybe that isn't even a factor to consider.....?

My midfi tube amp clearly pushes a band "behind" a vocalist, when listening in triode. Not in an unpleasant way, just different. R&R most of the time sounds more exciting in UL.  A Jazz ensemble with vocalist, seems more convincing in triode. Classical, I leave in UL.

crwindy,
the results partly depend on your speakers. What speakers do you have? db?

My Cary SLI-80 and Cary V12R tube amps definitely do not sound "dead" in Triode mode. I design/build my own custom speakers for fun and have tried various combos.  I've found less efficient speakers (87-89db) do sound better in UL mode with the stock or highly modified SLI-80. Once you go above 90-91+db speakers, you will start to notice more of a difference in Triode mode with your Cary SLI-80. Try it with some more efficient speakers -OR- bring your amp to a place with high efficiency speakers and re-evalute again. It’s possible your speakers are not a good match for your amp in any case. Try different combos before drawing final conclusions.  

I just replaced my Merlin VSMs with Vivid 1.5. 
I love the sound, and have no complaints. This was a question, as I didn't get the so called benefit of triode mode.
I wouldn't trade these speakers for quite a while. I am only at the house with them part time, and every time I go there I am shocked at how great they sound.

When switching between Triode and UltraLinear modes, do any of you speakers POP loudly ?  Mine does and the manufacturer says it's normal and pop-ing is dependent on speakers ! Not sure why... Regardless,  I worry about possible damage to speakers in the long term.

Same is true shutting down the integrated amp...  I first put it on standby mode for 2 minutes, then shut it down... POP !!!  and LOUD !  

To my ears, my SLI-80 siunds better in the UL mode. In the triode mode, it sounds flat and thin, but with better midrange. The speakers are Silverline Sonata-III.

My modified Consonance M800SE Monoblocks seem to sound a bit more dynamic in UL mode. This is with 89 db 2-way speakers. I had been running them in Triode for many years and recently switched. I find the difference depends on source material and usually is minor.

My Aric Audio amp is switchable also and I usually prefer triode.It's not thin sounding at all,the timbre is better but of course won't play as loudly.If I'm in the mood for a big dynamic sound I switch it back.I'm also betting more efficient speakers are needed.
I turn the amp off when switching modes per Aric's instructions.