Should I test my nitrites again? Or do you think my nitrate is just a false read?
Ok here goes.
Did you dose Ammonia back up to 2ppm and then retest 24 to 36 hours later?
If so did your Ammonia return to 0?
If it did then you're done your cycle.
Now to deal with the high nitrates, after doing the Ammonia trick, do a 75% (roughly) water change all at once. This will almost certainly bring your nitrates down to a range around 20 I would think. If it does, then add your fish and have fun.
My scenario: I reached 0ppm ammonia after 7 or 8 days. I dosed to 2ppm and it came down to 0 after 24 hours.
Meanwhile my nitrates were hovering around 80ppm! Aaaaaaand my nitrites were almost 2ppm. I left the tank for another 2 weeks fretting about the nitrites which were stuck at 2ppm, then I researched and found that nitrites at that level are irrelevant in a SW aquarium. So, relieved, I did an 80% water change which brought my nitrates down to around 20 and I added my first 2 fish.
btw...my nitrites continued to read 2ppm for 6 weeks before they finally hit zero.
Since that time my nitrates are between 10 and 15 ppm and I have no skimmer nor refugium.
Have at it brother!!

I hope this helps in some way.
and a side note
@brandon429 is very passionate and knowledgeable about this subject and is an extremely valuable resource, however can be incredibly confusing at the same time LOL!