I have a 120 gallon w/ a 50 gallon sump/refugium and I don't skim. I've been skimmerless for 5 or 6 years, and I'll do water changes but not weekly or even bi-weekly. I've always gotten slammed for touting that I don't use a skimmer, but I don't care. For all of my filtration, I use 100 micron filter socks and a pretty decent size fuge, and live rock. That's it.
All this being said - I've recently figured out that my 10-year-old LR has become a phosphate sink and I'm in the process of getting ready to swap it all out. My tank looks terrible with hair algae but all corals are fine.
I do NOT notice particularly fast growth with my zoas. Softies seem to thrive, and SPS would grow until I got FTN last summer while not paying attention to the tank (we moved), but I've never had fast-growing zoas in my tank. yes, they grow, but not at a tremendous rate or anything.
I've had some zoa colonies/frags for 6-7 years, now. I have RPE's that I know I bought in 2004. They've always been good. My big problem with zoas is that the light has always seemed too bright. If i put any of mine even halfway up in my rock, they close up, and will die if I keep them there for more than a week or two. Put them back down on the floor, and all is well. I'm only running four T5's, too. Only one of the four t5's is a daylight bulb, the others are towards the blue side of the spectrum. Not very bright at all, IMO.