lets see...first of all this is just my advice i am by no means as experienced as some but i've recently gone through some major gear overhauls so i feel i can lend some decent tips

with your budget its going to be hard to get a down bag and jacket...your avg 20F bag will cost you at least 100...i have the kelty light year xp 40...i love the bag..it comes in a 20F version and you could always pick up a fleece liner for the extra chilly nights(i'm an east coast boy not familiar with the YNP climate)

down jackets are certainly nice but expensive...you may find suitable ways to stay warm with layers and your budget...

I lately have been using under armour heat gear compression shirts as my on skin base layer...tank

if it gets a lil colder i throw on a long sleeve heat gear non compression UA shirt...

colder yet a compression cold gear shirt by UA...if your active and moving around this setup under a lightweight windbreaker or jacket...you will be warm

i think the shirts cost 25 - 40 - 65 respectively...

for cold weather i have a very technical ski shell from north face - free thinker jacket...but it kills your budget

maybe invest in a lower price waterproof shell and some merino sweater and layers for your down alternative (i live check to check i know the income/gear struggle) and i do plenty of winter camping this way and i have zero down in any gear

do you have all your own essentials...like soap, medicines, cups, cutlery, compass, food bag(guides?)...all that little stuff? i like to make tea in my titanium mup at night...and for dinner i take gatorade powder for 1L nalgene as some flavor after camelbak flavored water all day...

the trekking poles btw are awesome...i just started using them this summer and they are defintly useful on descents and ascents, and i sort of like them on level ground just for even strides etc...i got a pair of black diamonds for 80 bucks...worth it imho

do you have water storage/bladder for your pack?
water filter?
first aid?
pot needed for stove?
don't forget a rain cover or extra garbage bag too...
camera?!?!?
headlamp or flashlight?