Don’t be afraid to call a pickup maker and talk to them about it. They can give you insight and offer suggestions based on guitar, styles, amp types.
Does the guitar sound good unplugged? I’ve discovered that a guitar that sounds dead and lifeless acoustically delivers tone that is DOA at the amp. YMMV, but that’s been consistent for me.
You say the pickup sounds muddy and compressed, which point to an overwound pickup type. As a general rule, hotter pickups sound more midrangey and compressed, and lower output types tend to sound brighter and less compressed. In your case, you might try lowering the pickup away from the strings as a way to tame some of the output and clean them up a bit.
I have found that I like the sound of pickups wound more like early PAFs and T-Tops that Gibson did late 50s to early 70s. They are clear and open sounding and can be boosted with a pedal to hit the front of the amp harder when you want. They are useful in all positions, and you can get many tones with just the pickups and controls. Once I figured that out, I looked for pickups with those characteristics. You will need to run down those “what I like and don’t like” questions, and it’ll narrow your searches considerably.
By the way, everybody has a favorite pickup type, brand, or philosophy. I never had any success paddling in that river. Take in the info, use what’s useful, then find your own way.