I have been happy with the Streamlight Sidewinder Compact. I covers all your criteria except rechargeable, but I suppose you could use a rechargeable Surefire CR123.
TAB Gear for my TBAC Ultra 7 on bolt guns.
Armageddon Gear for my Sandman S on gas guns.
The TAB Gear is the nicer of the two. Bought them because that's what Mile High Shooting carries.
For gloves, I use PIG Alpha gloves most of the time or their insulated cold weather glove if it's frigid. I like them because the are designed for dexterity and shooting and they frequently go on sale at SKD.
I've carried a Leatherman Style PS and Gerber Impromptu on hundreds of trips for the past decade without issue. Keep in mind that the Style PS is only good for very light duty tasks.
My favorite layering combo the past few years, including WY antelope last fall, is Peloton 200 hoody, Kenai vest, and Chugach rain jacket. I got the vest as an impulse buy during a sale with no expectations, but now it's always in my pack. I still carry a puffy, but the Kenai is all I need most...
For down, take a look at the Montbell Superior Down Parka. Only $200 and very close in specs to the Kuiu Super Down Ultra.
The Kenai would be my pick for synthetic. I have the vest and used it for a spring turkey hunt in Humboldt County last year and it was great. It is actually warmer than the...