I would only run carbon if I needed too... sometimes if my daughter is burning incense or something or if I am doing a bunch of work in the tank I'll run a touch of it for a day or 2. Probably doesn't do anything, but I keep some on hand for potential "toxins." That said I burn a candle in my fish room every night almost and nothing happens. I will also run some if we are having a party or something and I want the water extra super crystal clear to show it off, but then I take it out. It's just unnecessary IMO. The one exception I make is if I'm breaking in a new tank. I will run if for a week or so to grab any bad juju off the rocks I'm using (always live and pre-cycled BTW). I just run it for a week or 2 passively while the tank settles. This is all probably totally unnecessary. The 2 most successful tanks I have seen IRL run only a skimmer and socks, and to regular WC. These are folks who have very long term (decades) of success and sell high-end SPS. As far is the matrix... I'm not gonna lie, I don't even know what that is. I'm assuming its like marine pure spheres or something. You probably don't need it. I keep some spheres in my sump just to seed future projects or for emergency purposes, but I'm just putting usable rocks in there more so now. I dunno... maybe take some out? Dude, I don't test ammonia.... ever. I don't even test in the beginning. I let the tank run with mature live rock and throw in some water from an established tank and basically thats it... then I just add slowly until I know its good.
Your bacteria population is probably fine, but I'm not a marine biologist. I would take it out, run some floss and polishing pad, and keep some media handy for any creeping emergency... then, reevaluate. Good housekeeping is probably all you are going to need if you stock correctly.