Business School Worth it or Necessary to go From Growth to Buyout?

Hi everyone - I'm trying to figure out what I want to do next year. I'm currently an Associate at one of the top growth shops folks talk about on here and I think I would like to eventually move to a more traditional buyout role in the future or try move to a megafund but stay within my same strategy. I spend most of my time sourcing but situationally execute on banker processes and sourced deals as well.

I graduated from an Ivy with a good GPA and a non-traditional background that I know adcoms will look at favorably. I also have business school funded. However, I'm not confident in my ability to get a competitive GRE or GMAT score because I'm a poor test taker. I'm hoping to clear 320 on the GRE but studying has been a slog.

Curious to hear everyone's thoughts - is business school necessary to move to a larger buyout shop? I know it isn't if I want to stay in growth. Additionally, is it even worth it to attend business school at all if I can't get accepted to H/S/W? Part of me wants to go just because I think it would be fun and interesting and allow me to explore different types of investing through internships, especially since it's paid for, but I'm already older because of my non-traditional background and I don't want to necessarily lengthen the time it takes me to hit VP and give up solid senior associate comp if I don't have to.