Switching amps won't solve a problem like this, unless the original amp was broken or an old/cheap load dependent class D. EQ can solve this, but the statement
is kinda weird, because there isn't one EQ in higher frequencies. There's a near infinite number of setting combinations so you couldn't possibly judge them all by testing a handful or even just a single one.
That being said, your room with a wood ceiling, laminate flooring and no big windows looks pretty good to me. I would recommend you start with two simple things: Rotate the speakers outwards in 5° steps and see if that reduces the hot treble. If this doesn't help, add a medium sized carpet in front of the speakers and below the table. You could just borrow one from another room or use a big blanket for testing.
If both of those options fail, you can think about EQ. Due to the amount of options an EQ gives you, it is very powerful but can also be time consuming and tedious to tune. That's why I would initially recommend the two "easier" steps above.