I think you've missed some tools which are already in place to do exactly what you're seeking. Click the Investing heading in the left sidebar. Click Portfolio. Set the date you want to see. Make sure the filters are set for “Portfolio Value” and “By Account”. And there you have it: the portfolio view shows you your account balances as of the selected date.
Alternatively, you can just open a Net Worth report. It does exactly what you want: shows the value of each account as of a specified date. (The default Net Worth report shows all accounts, but you can customize and save one which just shows your investment accounts if you wish.) Just open the report, click edit, enter the date, and there's your report.
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