Need to create a vacation tracker for 350+ employees

We currently track vacations in three ways - a book with a sheet in it for each employee, a calendar in email for making sure people aren't overlapping, and the physical request form for making sure employees get paid at the right time for their vacation. I am trying to combine all these functions into one spreadsheet (since we don't have any kind of HRIS program) and I'm getting stuck, even when I give up trying to get the last one in.

I'm using the Employee attendance tracker template, and it's almost exactly what I want, in that it shows how many vacation days are used, how many are left, and has tabs for each quarter so individual days can be marked off (which combines the first and second functions into one). HOWEVER, our employees vacation resets on their anniversary date, not a calendar, so it's not working as is.

Does anyone have suggestions for tracking vacations by anniversary date in Excel? I tried adding extra tabs for previous and future quarters and noting the hiring date, but I run into problems when an employee schedules time far in advance, after their anniversary date. (Ex. it's July, an employee resets in September, and submits requests for August and November.)

I'm in luck (I suppose) in that I'm not worried about accrual or any other kind of leave, but I fear I'm stuck with paper forever since we have no budget for software. I attached what I've got so far (with dummy information), and any suggestions would help.