If your nitrates are jumping so quickly could be that you are under filtered. If the filter is recommended for a 300l tank and yours is 350l that could be why your nitates are rising so fast. How many liters per hr is the filter rated for?
I don't think this would be why your fish are dying as mentioned you are keeping the nitrates well under what is considered harmful to fish but it is requiring a lot of large frequent water changes which makes me think you need another filter.
Sorry i know this prob doesn't help with your fish deaths, from what i have read you are definately doin all the right things, maybe worth lookin at dosing with prazi, not the best thing to do, treat your tank with meds when you don't really know what you are trying to treat but you are runnin outta options and prazi is fairly mild. Maybe worth a shot.