Most plants can handle a 3 day black out, however, you may want to remove the Betta.....if the hornwort is the main issue..remove it and toss....It is important to manual remove as much of the BGA that you can on a daily basis until you start the black out....you need to remove as much of the organic load that you can since this is feeding the bacteria...strong water movement is needed too.
I get this a couple of times a year in 2 of my NPT's...one that gets full sun and one that doesn't....I usually can get rid of it in about 5-10 days without doing a black out...just manual removal of the BGA daily along with about 20% water changes....I have noticed that the Florida Flag fish are eating it....I had read that they are one of the few fish that will..but do nothing for the hair algae like the research said they would....
I have a rain barrel that sits in direct sun all day that I keep piece of wood in to grow algae on that I use for my pleco tank-I swap it out as needed for all the baby plecos I have.....