Just to add to @Jon's suggestion… You don't need to run the Net Worth report weekly or keep a spreadsheet to do what you want. You can customize the Net Worth report to show your account balances week by week, so you'd only need to run this report at year-end, export to Excel, and get your Max values.
Choose any of the pre-built Net Worth reports, such as "Net Worth by Month" or "Net Worth", and then change the "Interval" above the column headings to "Week". (If you have any closed/zero accounts, you may want to go to Edit > Accounts and de-select them so they don't clutter your report with rows of zeros.)
The FBAR report is very simple: account name, date of max balance, max balance amount. It's more precise than the weekly net worth report, since an account could have peaked and declined between two weekly intervals in the net worth report.
I'm not familiar enough with what your reporting needs are to advise whether it's worth paying to upgrade to Premium just for this.
Take a look at the Net Worth report, it seems like that should be giving you the numbers you're looking for.
But the FBAR report might make your life easier, since you could just run that once at the end of the year and it will tell you the maximum balance of each account during the year and what date that occurred on. You wouldn't have to run weekly reports or keep a spreadsheet.
that will probably give me the max value and date for each account, not the aggregate value across a number of separate accounts
You're correct, it's on an account by account basis. That seems to be what the IRS wants, but I have no personal experience with FBAR reporting so I'll leave it at that.