The was my experience:
My setup was very similar to yours. I tired a couple of the "reef safe" remedies to no avail. This is the make or break period for beginning reef keepers. Here's what I've experienced and what I learned from my mistake:
Cause of the ich? Tank not mature enough to support the marine life. Too many fish, too soon, for a tank that wasn't ready for any fish. The result was fish stress, leading to ich. What happened to the fish. Dead.
What did I do wrong? Impatience.
What did I do to remedy? I let the tank sit fishless for a minimum of two months. Why? First the obvious: no fish, no Ich. The Ich parasite must have vulnerable host to propagate to an "infestation". Second, this will allow your tank to mature to a stable environment. If you keep up with some regular maintenance as if there were fish in the tank then you'll find that the beneficial organisms provided by the LS and LR will start to "do their thing" and help to stabilize the environment making it less susceptible to radical chemical swings from minor changes.
What did I learn? Take things very slow. It seems that experienced reefers can work around this time limitation. I’d like to learn their methods some day, but I’m sure their experience came at a hefty price tag. For me there’s no other way than to make very small incremental changes to a maturing tank (3-4 month break-in) with organism that are hardy and benefit the maturation process. I don’t profess I know all of the changes that happen, I just know that time was my best friend. Quick changes in the environment, including the inhabitants, will always upset the balance of the ecosystem in the tank. Then trick is to not over do it.
Your tank need not sit empty. Get a cleaner crew with snail, crabs, shrimp, feather dusters, maybe a brittle star or two. These are not acceptable ich hosts (they won’t get it) and they’ll play a role in maturing your tank. This will also provide some entertainment while the tank is sitting empty. After the tank has sat at a couple of months, add a couple of ich resistant fish like a Gobie or Blenny. Watch them carefully for stress. If they don’t adapt to your tank quickly, you’ll need to let things sit a little longer. Definitely do not do something silly like add a Tang or Angle a couple of weeks after you had an ich outbreak. That’s simply fish homicide.
Unfortunately your fish will likely die unless you remove the LR and get them in to a copper medicated hospital tank. DO NOT ADD COPPER BASED MEDICINE TO YOUR TANK.
I was patient and did exactly what I talked about above and the same tank is now almost 18 months old with a thriving community of animals. I’m starting on my second reef twice the size and feel much more comfortable about the process.
You will get other opinions from garlic to complete system breakdown and sterilization. All I know is this worked and I continue to apply it.