It doesn’t fit every single one of your qualifications, as it can only come on instantly to the memorized mode or the the highest level or to strobe mode, but the Nitecore i4000R fits all of the other ones I think. It uses a 5000mah 21700 battery, but can also use 2xCR123 batteries, and it comes with a sleeve so they don’t rattle.
It also comes with a holster that looks useful for law enforcement , and much more effective and easy to get the light out of, than your average nylon holster.
Here’s a link to a review of the light:
https://budgetlightforum.com/t/-/61004
There was also a coupon or group buy for it on here, which made it $90 instead of $120 I think.