If you have Brass Tailpiece Studs you can probably brighten up that guitar by removing them and replacing with Steel Tailpiece Studs. On my 2011 R7 the long steel studs from RetroSpec brought on the most active top end within the steel studs that I tried.
If your Tailpiece Studs are non-magnetic they are probably brass.
You can also check the ABR-1 Thumbwheels, and if they are brass, you could try steel wheels. I don't recall what came stock on the 2006s.
Hardware changes like this can have significant effects upon a guitars' overall voice.
Also +1 for RS Superpots for volumes. If your wiring is stock then your tone pots are linear taper. Replace them with CTS audio taper 500k pots it will have greater usable range. And also change wiring to '50s - capacitor connected to middle lug on volume pot instead of leftmost one. ( 2 Superpots 500k + 2 CTS audio 500k -> ~ 50$)
pickups adjustment : lower the pickups BUT at the same time bring screw poles UP - that will take some body off the tone but keep the highs.
I have not used Retrospec steel studs (yet) but Faber steel studs (~20$) for tailpiece will also do the trick. Also if your ABR-1 bridge is stock it is the older version WITH retainer wire for saddles. Replacing it with new version of Gibson ABR-1 (~60$) which is wireless (no retainer wire) AND using thumbwheels that come with new version (made of steel, smaller and thinner) will also remove some muddiness.
So, it's both hardware AND electronics. This all BEFORE you even consider changing pickups. And pots, bridge and studs are the price of just one pickup worth buying as a replacement. And these 3 might be sufficient, so you might not need replacment pickups at all.
+1!Your pots are probably stock and too low of a value. Buy some RS Guitar works "super pots" for your volume controls. They are around 550k of resistance and will brighten your tone considerably. (higher resistance = brighter tone). Plus you'll like the taper of the pots compared to the stock historic pots.
Caps wont change a thing unless you are someone who plays with your tone knob and even then the difference will be minimal. Its more affecting the "midrange" not brightness.
Try lowering your pickups...but I doubt that will do much. It may help clear the mud. Just take a screwdriver and back off each side of your pickups 2 complete revolutions. If you like the tone better (it should be a bit less muddy but not necessarily "brighter") then do some fine tuning from there. If not...put it back.
For fun, if you order...measure your pots when you take them out and measure the RS pots. I did this recently to a LP I had. 1 stock pickup was around 450k, the other was 498k. Each RS pot was 544k on the nuts. Really brightened the tone.