Yeah - this sort of bouncing around can cause all sorts of issues with the sort of organisms you want to keep, and once they get out of whack, it creates an opportunity for this sort of crud - and dry rock tanks and low surface competition let it get out of control real quick. And once it's out of control, it becomes really difficult to deal with it via nutrients/etc, because its healthier than your corals/etc.
I think this is lyngba, but if you know someone who has a microscope, or feel like spending $50 on amazon, confirmation would be good (but not 100% necessary).
I'm a little concerned looking at this with how little non-green color I see on the rock for a year and a half old tank - are the photos just deceptive? Or did the crud just overrun everything?
I had an issue with Lyngba in the current (well, pre upgrade) tank a year or so back that I had the hardest time figuring out - and it turned out that my Nyos nitrate kit was trash, and it was bottoming out the nitrates for a month or so that started it.
I think you're mostly doing the right things right now - keep the PO4/NO3 in the .1ppm/10ppm -ish range, and do as much as you can to deal with this stuff mechanically. The big issue here is the stuff can grow from broken pieces, so anything you do, you want to do in a bucket, or with a siphon close.
Wear gloves because this stuff bothers some people's skin, and continued exposure is usually how that starts.
As far as critters - mexican turbos get enormous (the zebra ones), and are bulldozers, but they're the animals I've had the best luck with for pretty much everything.
Bubble algae can be a pain - and you should remove it when you can - but it generally doesn't kill corals the way hair or lyngba can - it's not rubbing up against them irritating them all day. And fast growing corals will grow right over it.
This is really it - the goal for any sort of algae eradication is to hamstring the algae long enough that the animals you want growing are growing well, and then they'll do the work for you. Healthy coralline is chemically brutal stuff - and I'm sure you've seen healthy sps burn their way across a rock - you get that white ring around them (outside the growth ring) that's just bare rock where they've chemically killed everything.
In a tank where the corals and coralline aren't doing well (because nutrients got all messed up), hair algae will smother and kill stuff. In a tank where corals are growing well, they'll burn their way right through it.
I like to use the analogy of weeds in a garden - you can't just go in there and rob the place of all nutrients/deprive it of water/sun/etc - because you'll kill the tomatoes and cucumbers - and once you kill them, the weeds come back better than before. You need to pull and cut the weeds to hamstring their growth, and give the cucumbers and tomatoes everything they need, so they can shade out the weeds, and fill your planter with root mass. It doesn't matter how many times, or how well you kill the weeds if you don't get the other stuff to take their place. They'll just come back.
Its hard, but it's the only thing that actually works and doesn't just look like its working for a month and then swing you into some other weird problem.
You'll see big healthy reef tank with high nitrates and phosphates - and no algae - and this is because there's just no hospitable room for algae to grow, and the corals and coralline outcompete the algae for a bunch of micronutrients. When you drop dry rock in these tanks - it explodes with algae - and then very quickly gets overrun with coralline and then corals. It takes like 6 weeks for a bare piece of rock to go through that full succession - it's crazy to watch if you've never dealt with a healthy mature reef.