JBL 4367 shoutiness remedies?

A quote from the Measurements section of a Professional review on your speakers" There is a very mild upper treble reduction beyond 13 kHz but this is typical for most speakers in room. The entire midrange to lower treble area is exceptionally flat and well behaved. The bass region shows a gentle lift from room gain at 150 Hz down to almost 30 Hz where it begins to gradually roll of".....
 I suspect any shoutiness is either room acoustics/positioning or simply Class D being highly exposed by very sensitive speakers...How about cables,it's possible something in the cable chain doesn't like the combination of electronics & speakers...The fact that it's NOT every song that has shoutiness might also suggest you are simply hearing what is on the recording & those specific recordings are mixed hot..Can you compare between a CD & a streaming feed the same songs?

This may be a situation where the speakers are exciting the walls in your low ceiling apartment, in other words its the room acoustics doing the shouting. You could check this by setting the system up outdoors or in another room and compare.

In any case there is a simple effective and inexpensive solution- Owens Corning 703 acoustic panel. https://www.amazon.com/Owens-Corning-Fiberglas-Acoustic-Insulation/dp/B07XTMRQHQ/ref=pd_sbs_267_3/14...
You may be able to find this or similar in hardware stores. You will only need one to maybe three sheets. They come 48x24 and cut lengthwise 48x12 (or 48x8) they can be pinned in the corners like this (see picture #24) https://systems.audiogon.com/systems/8367

OC703 cuts easily with a knife, and is so light weight you can pin or staple to the walls. Bevel the edges so it fits nice and neat, then wrap with fabric or spray paint so it looks better.

I had a similar problem in my room where certain vocals would excite this region and be unnaturally loud. As I recall Holly Cole was good at this, with certain vowels and certain notes held a while being the worst. This simple trick was the end of that.

Being where you are if you can’t find OC703 and don’t want to order a lot be aware any similar damping material will work so long as its placed in the corners like in my room. This works on the principle the walls and ceiling act like a horn that amplifies any sound coming from the corners. So eliminate any sound coming from the corners and you greatly reduce the problem without using a great deal of damping material, which would also solve the problem but make your room way too dead in the process.

I can help you. Please pack up your JBL 4367s and send them to me. Problem solved.

But seriously, these are about the least "shouty" horns you will ever hear. I agree with what freedivr and squeak_king_77 suggested.

If it were me (please re-read my first paragraph) I would never mate these speakers to Class D amplification. I would use tubes but there I have heard several solid state amps sound great w/ JBL horns. I'm thinking Luxman or Accuphase Class A or even McIntosh if you like the mac sound. I once heard a pair of JBL 4430s played through a rebuilt/ upgraded Moscode 600. Sounded great.

If you are handy at all with a soldering iron, I would change out the parts in the crossover to higher quality. Ask the dealer or JBL directly for the crossover diagram/schematic. Should be pretty easy to find cap and inductor values. Seems I’ve read an internet article or two on that specific upgrade. https://www.audiosciencereview.com/forum/index.php?threads/jbl-4367-inside-photos-video.2293/page-2

https://positive-feedback.com/high-fidelity/jbl-4367-studio-monitor/    One comment to this review "These deserve Kenrick Sound Outboard Crossover upgrades from Japan.."