OP
{exec sum: stay for the few months}
at only 44 (maybe 45 when you leave) you have 20 years to Medicare for health insurance.... $400k would certainly go a long way towards that need. Also, if you leave early in the new year... you've got enough for a maxed out SS year... don't know where you are relative to the second bend point but it would get you closer... so it would impact future SS (you and spouse)
As you mention that the value is after tax...
and at that type of comp level I'm presuming Bay Area (since car was mentioned) or NY, so either would mean that half is lost to taxes I know for me it would be hard to pass up at that young age as it allows for some serious splurge at a time when you can presumably easily enjoy them. or it allows for some great gifting over the next years to kids that will further set them up.
From a w@rk perspective, I'd be trying to insure that your team is well set up for the transition (I know that I had fully completed everything for hand off when I left, with full documentation etc so any missteps weren't on me (and the knowledgeable ones knew that). I'd be more concerned if I was the principal engineer (or whatever) that might have been required to bid on an RFP or the like (It's clear that you aren't a C-suite since there would have been stipulations on departure (SEC requirements, etc)... as that might have a serious trickle down effect on those that you leave behind.
On a practical note: Jan 1, 2022 is a Saturday so it's likely that the following monday would be a holiday for you so that your first day in the next year is January 4th (late enough to insure that you clearly are over the finish line for vesting/payment). As a bonus, you might even either have December 31 off or leave early!! In that vein, I'd be having a very nice new year's
The other thing, leaving in September doesn't gain you that much good weather versus January, just less driving in some bad weather (many areas are worse after January, as it's colder, although some areas have higher snow earlier... it's too cold to snow later...BTDT). Cruises and the like might be cheaper and less crowded on the shoulder season... think of a nice New Zealand or Australia trip
I'd be putting notice in, say Jan 5, and would have directed everything to the 401k for whatever paycheck you would get in that period...you'll already max out OASDI due to your payout so in that way it won't have any effect tax wise whatever you do.