I hung around the GT threads most of this past year (son applied there) and I had the impression that the big scholarships were very competitive.
Last year GT was on Common App and had some GT-specific questions. It took my son some time to do because it was his only common App school.
I can’t remember if the scholarship apps were additional essays (son didn’t apply for those - I just remember reading some of the posts here of other students who were in the running).
You might want to peruse some of the school forums here and see if you can pick up how time-consuming and how competitive the scholarship apps are.
You are wise to pick your battles and set a strategy this summer.