That's right. It's a new tank, but it ran for about a month with those lights and without the CO2, with very little algae. Adding the co2 was definitely the catalyst for the algae bloom.
Unlikely, It takes a while for algae to really develop before it becomes very visible and a nusiance, probably just a timing thing more than anything else.
A tank isn't like a jigsaw puzzle where you can add pieces as you go along. You have aquasoil and high light without co2, that's a algae incubator, it just had to develop.
BTW any stirring op of the aquasoil will realize ungodly anounts of ammonia etc into the water column so if you did that it would certainly make it worse.
I would do lot of water changes, trim, cut lights back to 4 hrs, use carbon or other organic removal media and yes use co2.