The best way to attack that nitrate problem is to do a one time 50% water change then do another 50% the next day. It'll export those nutrients and help get your alk back to normal. Then I'd monitor your no3 levels to see if and how fast they return to the original levels. But, if your tank's 150+ gallons this may not be feasible.

You mentioned your skimmer has a drain. Does that mean you still check and clean the collection cup every few days? If not, then try to start doing this. It'll help with the doc's before they become nitrates.

Also, a cannister with some rowaphos or other phos remover may help with phosphates and silcates. These are just a few things that have helped me. Not sure if they apply to your situation.