Your speakers will produce 91 decibels at one meter distance with one watt. It’s just simple science. So depending on how many meters back from the speakers you sit, and how you measured the volume level of 93-95 decibels(or were you guessing?), the Parasound amp is putting out 2-8 watts or so per channel. It’s not straining, believe me.
What is possible is that you don’t like the sound of either the Parasound amp, or the speakers, or the result of the combination of the two. But that amp is not straining.
You mentioned having another system, perhaps you could pair your Triton 2 speakers to that amp, and see if you prefer that sound, if you haven’t already. If you like it better than the Parasound, then buy the other brand.