Nitrates will take the longest to work off. :doubt: It took me about 5 months or so to work off just 7 or so ppm of nitrates and that's with a very small bioload (4 small fish in a 75gal), weekly water changes of 10-15%, 24/7 skimming etc. Good sized water changes using ro/di water will help dilute the nitrate issue some, but you will need to find the source of your excess nitrates. Are you running a sand bed? If so, what type?? (ie shallow sand bed or deep sand bed?) If shallow sand bed, do you vaccum the substrate when doing your water changes?? If not, that could be part of your problem as waste can easily get trapped in your sandbed and cause nitrate issues. I ended up tossing my sandbed for this same reason and going bare bottom. Helped quite a bit, but it is a look that takes some getting use to. Also, you mentioned your canister filter. Yes, they can cause issues like mentioned. The bio-material you have in it, I would get rid of. It will not provide anything extra for you that your liverock won't provide. Bi-weekly cleaning of it IMO is too long as well
To keep waste buildup from working against you, you'd want to clean those pads every 2-3 days which can be a pain. This is the same reason I didn't put anything in my canister filter when I used one other than carbon because of the waste build up that resulted. Eventually, I tossed the canister filter itself and just hung a bag of carbon in my sump because of the waste that just accumilated in the canister. If you notice when cleaning your canister, a lot of waste will even just sit on the bottom of it which can cause issues. The main thing with any tank is you want to get rid of any waste before it can cause any issues for you and this is why people adopt different methods like skimming, frequent water changes (we have a member here that did a 100% water change on his tank every week!), good husbandry, good flow with proper placement to keep all waste and detritus in suspension to be either used up by corals or removed via skimmer or mechanical filter etc. and so forth.
With that said, what you are experiencing is normal and happens to almost everyone after setting up a new tank. Tanks need time to mature and during this time you will experience algae outbreaks from time to time. Your liverock will have to build up all of the necessary anaerobic bacteria to perform denitrification (process by which nitrates are converted to nitrogen gas) which un-fortunately can take some time so don't get too stumped as it should eventually pass. You could possibly try and manually remove some of the algae from your tank as in doing so, you will be exporting any bound-up excess nutrients.