I would say that tangs and angels in a 140g is too small. Unless you are talking dwarf angels. Tangs can fowl up the water quickly and so can angels. Get yourself a ammonia badge (seachem) just as an extra precaution. To me it sounds like a environmental issue. The environment will effect stress in the fish making it susceptible to all the diseases mentioned.
You say dry rock, but it should have been turned to live at this point. You should be getting really good biological filtration after two years. I would add a protein skimmer to help with particulates, but make sure the rocks is set for the particular species you are looking at. Make sure you are adding compatible fish and in the correct order. Make sure you are buying from a reputable supplier. Make triple sure you are giving the correct foods for the fish.
A UV is only good if the bulbs are changed frequently and the flow through them is correctly done. Otherwise, they do nothing, so double check this too. Your parameters from Ammonia, nitrite and nitrate look fine, but keep an eye on them. The badge will help a lot.
Careful putting meds in the tank unless you are prepared for the loss of biological filtration.
I will say, depending on type of tangs and angels, you are setting up for failure. If this is your first dive into saltwater, try more tolerant fish first and work your way up to what you want. Patience is key and experience is everything!