So take the entire week of 8/10 off via PTO = 40 hrs.
Then on the week of 8/17, take 24 PTO hrs. off (which = Monday thru Wednesday, full days.) Submit it for your PL's approval, and take a screenshot of the approval before you take the PTO.
Then just "call in sick" for Thursday & Friday.
And take more "sick" days off, one or two at a time, weekly, until you leave!
You don't need a doctor's note for 1 or 2 days' sick leave at a time, and there's no limit on using what you've accrued, even if it just happens to be more often than you're usually "sick".
And you don't need your PL's approval for taking sick days, either.
If your PL presses you for why you just happen to be "out sick" even after taking almost a full 2 weeks of PTO, tell them the VSP situation has been making you so stressed out, that you're literally physically ill about it. They don't need to know details, and you aren't obligated to provide them with any.
LOL
But really, you have to look at it as a blessing that you're getting out with VSP $, AND out on the first wave of the September departure date. Try not to mourn the loss of accrued time off, look at it as you've been gifted with collecting much more $$ on the way out, AND that they're paying YOU to liberate yourself from their toxic, sick environment!