I think you have two “problems”. The "algae" in the sand and the growth on the rocks. However – the solution of each problem is probably opposite each other. I´m not sure off the stuff in the sand, cyano,dino or diatoms but when I got stuff like that – it has normal been in low nutrient environment (low in PO4 or/and NO3) in aquariums with low biological diversity. The way I have gone here have been to rise the biodiversity (even the microbial diversity) and rise nutrient into readable figures (PO4 around 0.04 -0.08 and NO3 around 2 – 4 ppm) if my “sand stirrers” not done their job – I usually help them once a day with a stick, stirring the sand.
The classic way to handle the growth on the stones is to limit the nutrients in the aquarium – a strategy that´s just the opposite the strategy above.
This is a dilemma and I think you will have to think outside the box. The first problem is – IMO – the most difficult to handle in more than one way (dino and cyanobacteria have very few natural grazers) – I would slowly rise the inorganic nutrient level in the water column and try to rise the biodiversity in the sand
If you can read figures – you know that´s no lack of nutrients.
How to solve the expected microalgae growth on your stones? The answer of that is to rise the amount/diversity of your CUC. As I can see on the pictures you have few (or no) corals that can compete with the algae. With that type of algae that I can see on your rocks – I think that hermits and urchins is the best type of CUC but even some snails will help. IMO – in a tank of your size and no/few corals in the DT – at least 30 hermits and snail and a couple of diadema spp urchins will do a good job. Try to take as many species of hermits and snails as possible – because different species have different food preference. The urchins will eat some of your coralline algae too but in the beginning – they are useful tools in order to eat up the algae you have problems with at the moment. When they have done their job – just take the out from the display and start to grow corallines on the microalgae free areas.
What I´m tying to say is that you should identify the most important problem at the moment – defeat that and at the same time try to prevent new problems from arising. Take it slowly and methodically
With rocks looking the way your rocks look – no problems with food for hermits and urchins – when they have graze on the present algae fauna – new algae will arise – small green algae that will be food for algae eating snails
Because you have had problems with surviving rate of snails – you can wait some time with them (until hermits and urchins have done their work). However newly imported snails can have low surviving rate
Sincerely Lasse