I want to support the approach suggested by Evan (Waterbear )

With your CYA levels way up at 125 you're going to need to shock at very high levels to get it effective and then continue to hold quite high levels all summer.

You've got to get rid of the algae and the easiest way to start is to pump half of it our and get your CYA levels down to an reasonable level at the same time.

I just wrote up the plan under the heading CYA help a few lines from your posting on this thread.

If the pool is concrete and you don't have a ground water level problem, you could brush and then vacuum to waste and you'll get rid of a huge amount of the algae before you start spending money on chemicals.

And I'd save the algecide until its clean. Chlorine will work better and cheaper at cleaning up the mess. Use polyquat if you think you must, as a preventative. Many of us on the list only use polyquat in a double dose for winterizing to avoid the mess you're openning to.

Good luck