UL compass suggestions

Compasses aren't heavy. IIRC, my Suunto MC-2G weighs 2.4oz. Pick a compass you can use with good accuracy rather than stressing over the weight. I like a mirrored compass and the multi-purpose uses of the mirror, but a good baseplate compass like the MC-3 doesn't weigh enough to make any real difference in your base weight.

As a general philosophy, there are some items in your kit that your life can depend on. Getting crazy light is an interesting exercise, but the stuff needs to work when needed. Headlamps are on that list too.

The Polaris looks fine, similar to the Suunto A-10, which is 0.986oz with a little spectra cord. If you wanted to, of course, you could take a Dremel sanding drum to it and get it down to perhaps 0.6oz or so.

However, if I need something more precise for actual off-trail navigation, I prefer the Suunto M3G because it has a separate declination adjustment and that natty double-gimbaled needle, which IMHO does provide some practical value because it settles quickly and precisely even when the base plate is farther off level than a comparable non-global-needle model. And it has the inclinometer. It weighs 1.62oz without the cord.

This all assumes you know the local declination, without which all the results are going to be ballpark at best! (Unless you happen to be following that wavy little stripe of zero declination.)

EDIT: very handy online declination calculator

The baseplate is just a shade larger than what I use and my wife uses. A slightly shorter baseplate would be fine.
Anything bigger or more fancy is just excess weight imho. I know lots of more fancy ones are sold – at a higher price of course.
However, a smaller dial is not nearly as good. The needle does need to be about that big.

Cheers