So… let’s assume there is in fact some change to the audio when the hats come in. If you take the part with only the kick drum, move it over to the part with the hats so that the kick drums line up precisely, then invert one track, then the result should be the some audio with just the hats AND some leftover artefacts of the change in the kickdrum.

Sort of like:
kick + hat - kick = hat
"modified" kick + hat - kick = hat + "modification"

Here’s some pictures of what I did:

And here you can hear the resulting audio:

As you can hear, there is absolutely nothing indicating any change in the kick drum sound. I think someone already mentioned it, it could be just some masking psychoacoustics. You could try just removing or lowering the volume of the hat on the step of the kick, see if that does anything.

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