Cook it, baby!
No, this doesn't involve any ovens or anything.
All you need is a bucket, 2 Rubbermaid containers, a heater, a powerhead, water, salt mix, a big brush and a lot of patience.
1. Put the LR in a bucket and scrub and swish it around in the tank water until the water's nasty dark.
2. Put it in a Rubbermaid container with new prepared SW that's the proper salinity and temp.
3. Put in a power head for circulation. Cover it leaving a crack for some air. Make sure it stays dark.
4. Repeat the swish/scrub after a week then put the LR back in another Rubbermaid container again with new SW.
The more you do this and the longer you do this, the cleaner the LR will become. Since nitrifying bacteria doesn't require light (like algae), you won't lose any of it. In fact, it'll multiply. Further, any remaining algae will die because it won't have any more nitrate/phosphate to feed upon because you've systematically scrubbed and swished it away.
I had a nasty cyano/hair algae problem in my tank last year. Pissed off, I tore the whole thing down and cooked the LR for about 6 weeks and it came out sparkling clean. Some people cook for months at a time.
The difference between simple curing and cooking is that you are actively depriving the algae of all the crap/light that it feeds on rather than just letting the LR sit in a tub of the stuff. Think of it as taking a shower versus taking a bath. The dirt goes down the drain as you shower whereas you soak in it while taking a bath.
Th