Fritz Algae Clean Out is the same active ingredient as Algaefix - an algaecide.
So just keep that in mind.
Your build thread mentioned a 12g tank and this being a 120g tank. Did you take the rock from the 12g? If so, assuming you put in a ton of new (dry?) rock to fill the space.
What does your clean up crew actually look like? Any sense of quantity of inverts? You mentioned tang(s) - how many?
My, opinion, is that using an algaecide isn't the end of the world. But you need to have something in place to prevent the algae from growing back -- so a healthy clean up crew, bacterial load, etc.
Reefcleaners would recommend a CUC sized like this for a 120 ->
https://www.reefcleaners.org/store/all-algae-crew-120-long-detail. The owner is also a great resource if you ping him and ask for suggestions.