Do I NEVER shut it off…?

What, no mention of cartridge warm-up?

i am bothered by two things in your question.  First the assertion that it must be left on constantly. Maybe, but i do not find this to be true with my own designs.  Rather i find a HUGE change in the first 30 minutes, a smaller change int he net hour and a decreasing benefit thereafter -- but your experience my very.
I will say that many of my designs have the low-power circuitry on 24x7 with no provision to be turned on and off - because it does improve sound ( and IMO, longevity).  But the power hungry output stages....my advice would be - experiment and list. Do it multiple times since perception can be affected by many environmental influences. 

My second concern is that it gets marginally too hot to touch.  Maybe i'm just conservative, but that sounds like poor design to me. Nothing i design runs too hot to touch.
Do your own testing.

My brother has the latest Diablo high bias in class A in part he  said shut off and then when listening it may take an hour to fully warn up.

I forget to mention if you have the digital card it will take much longer 
to warm up, my brothers  does not.