you are right about Kifaru and TiGoat being the best
I do think there Tipis are a bit over priced.
I am using a Kifaru Maga tarp with annex (I hand sewed in the annex)
Ask if they would do this for you, would save a lot of trouble.
its 750-770 grams(with 6 para cord guide lines 2' long) , and I carry 8 pags at 6 grams each,
and use trekking poles to set up, or if I need my poles and the tent is staying up, i use 2 sticks.
two people can stay in it just fine, with a stove and some gear(packs)
but that set up is about 40% more then your budget...
As for the stove, Im still looking into a lot of different ones, and haven't made up my mind.
one problem with the backpack stoves are the size, being small your limited to the wood you put in it (mostly dry small pine branches) they are small, old and dry. They dont offer a long burn times. so the stove needs to be watched, and fuel added no stop. to run bigger fresher wood with longer burn times you need a saw and hatched now where talking more weight.
the stove will take the chill off and is good for drying out, but not so for keeping the shelter plus 20 all night.
I did cover the shelter in pine branches and it kept the heat in longer but it took time to do, time away from hunting.
the Golite Shangra-Li 5, is almost 6 pounds!
the Oware Pyramid 9x9, is light and would work for what you have described
It probably is your best option...
Another option is build your own
I started playing around with TYVEK for ground sheets but theres lots you can do with it, watch a lot of the videos, and have some fun trying different things.