IMO, in a tank that deep, the mushrooms would need to be placed in the top half of the tank in order to do well.
Sun corals (tubastrea) are asymbiotic (no zooanthelae) and do not need any light. Each polyp needs to be individually fed vitamin enriched meaty foods (like mysis shrimp) several times a week in order to survive. If you don't mind feeding them they would do fine in your tank, but are not really a beginner coral.
I'd upgrade the lighting before getting corals. Look on-line for used equipment (you can also check the buy/sell forum). If you want SPS corals then you'll need to look into metal halides for the best results. Softies and many LPS will do fine with t5HO or power compacts.