Solder resistors to amp input/inside connector so that input impedance is lower. Between XLR - and + (or between RCA hot to ground if you use RCA input). Test with 10Kohm.
I have to thank you a lot. Your reply pointed me in the right direction. And the noise is completely gone!
Since you were writing about resistors, and lowering the input impedance, I went back to the Audiophonics website. Their Purifi amps have a custom input card with 3 gain settings. The default setting - according to their website - should be +20dB gain for a source signal of approx. 4.2V RMS. And that's the voltage of the balanced output of my Topping DX7Pro.
Audiophonics being a French company (sorry to all French people) I was concerned this may not be the actual default setting. And after opening the amp that feeling turned out to be right. It was set to "Configuration 2" for approx. 2.25V RMS. So I removed the gain jumper to get to the 4.2V RMS configuration. And gone was all the noise. Like magic.
Finally, I must say I'm a bit disappointed Audiophonics didn't point me in this direction. I raised a service request and told them about my setup. Not a single word about checking, let alone changing, the configuration. And since changing that configuration is not an obvious thing to do (changing jumpers inside the amplifier), it's not something a new user would immediately check.
Anyways, the amps are now dead quiet. And I'm very happy with my new setup.