FO tank huh? ok well lots of things here. were to start. first diatoms like silicates FIY. now lets start with your source water(tap), where your silicates are coming from. dont use it for a number of reasons, unless you have tested it for things like chlorine, copper and such aswell as phos, trates, silicates ect....yes using it will result in a continued algae issue, among other things. do use RO/DI, even most of those machines outside the supermarkets is a better way to go.
next your fluval and CC. with a CC bed and LR you dont need the fuval. it gets dirty pretty fast and needs to be cleanned often (once week). with no lighting bacteria will grow in the fuval and with lots of flow only aerobic grow. because of the nutrients collected aerobic bac will grow there first as it does not have to compete with algaes in the main tank, consequencially algae has less compention for nutrients in the tank. allow the bacteria to grow in the main tank and compete with the algae for surface area aswell as nutrients. this goes for the aquaclear also. if you want to use them for flow i would take out all the media. your CC needs a good cleaning too, about a 1/4 of it cleaned out weekly.
for a CUC you just have the wrong fish in there with the trigger, esp since its already established. it will just think its feeding time. might be able to get some snails, what type of trigger is it?
what i would do is stop using tap water(your main issue) and use RO/DI or RO but
NO TAP!!! that might be all you need to do but,
have you thought about ditching the fuval and aquaclear filters, add a pump on a closed loop and add a good skimmer. perhaps add some more LR. exchange the CC with sand aswell, you know go FOWLR setup. it just seems to me your wanting/going for a FOWLR setup instead of FO, JMO, could be wrong.