I have been in your EXACT situation before - 2x2 frag tank attached to large display tank. Display tank is algae free but frag tank grows algae like crazy. Parameters are all good -- anyways- Here is how you fix it.
Your cleanup crew and flow are TOTALLY inadequate. Don't change your lighting/light cycle, waste of time IMO.
First ditch the turbos and get a combination or ALL of these.
1 small yellow tang. smaller the better, plan to sell it/move it to your display tank once it gets too large. This fish will tackle fleshy algae.
1 medium/large lawnmower blenny. this will handle brown/green film algae and possibly also help with hair algae
10 blackfooted trochus snails - they breed and are very agile on frag racks
10 astrea snails - tend to stay on the outside of the tank walls
1 sixline wrasse - pest control
optional(emerald crabs for bubble algae)
optional(peppermints for aiptasia -- return them to the store when their job is done)
this cleanup crew will produce a lot of poop... next step... get the poop out of the frag tank with tons of flow! here is how...
1. First, If possible, increase the amount of flow going through the tank ... biggest return pump your overflow can handle is ideal.
2. Build an elevated frag rack about 4-5 inches off the bottom of the tank. Place at minimum two powerheads underneath the rack JUST blasting the bottom of the frag tank. If any snail poo/food/ditritus gets down here you want it stirred up into the water column constantly so that it goes into the overflow. Really important thing to note--- DO NOT GO SMALL-- 300gph powerheads wont cut it. evo 750/1050/1400 are what your looking for. I highly recommend you have them all on a wavemaker. In your situation with a 2x2 frag tank I would do 2 evo 1050's under the frag rack and 2 evo 750's over the frag rack providing flow for the corals. Depending on what type of corals you are growing you may have to change the 750's to something lower/higher power.