The higher P readings are probably because of a lack of bacteria and microfauna base in the sandbed that develop over time. Did you use aragonite sand?
The rocks look good and don't appear to have any issues from being mistreated by the prior owner and full of organics.
Cut back on messy feedings (pellets are much cleaner than frozen food if your fish will eat them), skim well, do water changes and wait for the tank to get established. A solidly constructed tank with real live rock, aragonite sand, good export (water changes and skimmer) and not being super-stocked can handle N and P on its own without any GFO or organic carbon... but it takes time. You can use LC or GFO, but if you do, those bacteria will not grow towards equilibrium in your tank and the onus to handle the P will be on you and not the tank. If you let the tank handle it, you need more patience, but it will eventually get to where it has "enough, but not too much of N and P." I know that this is an old school style of reefing without the gagetry, reefer involvement and new age tech, but it still works the best IMO.
Lastly, it can take more than a year for a tank to stabilize to the point that your SPS always look good. There are no shortcuts to this... any taken will be short lived IMO.
