Get yourself a unicorn to haul your mythical pack while you're hunting.
Seriously though, quality and lightweight costs money. If your price point is solid then I would suggest looking for used packs. A used Kuiu or Exo Mountain gear would be a great choice in that price range. Depending on the size of the pack you want, you may find a Stone Glacier as well.
I'll try to be somewhat constructive. You won't find a a quality "hunting" pack manufacture and I mean those that are making truly lightweight packs for under $300. You might find some of them used. I would suggest you look into a "backpacking" pack that isn't marketed for hunting. Most are extremely light and actually do a fine job. My bro in Alaska uses these and has hauled a lot of sheep long distances with them with success. I believe his is a MountainSmith brand.
Like others have said, you're going to have a hard time finding quality and lightweight at your price range. If you really need to stay below $300 get a backpacking pack from Osprey, Gregory, REI, etc. It will function better for hauling loads than any cheapo hunting pack. Your other option would be to scour the classified threads on several hunting forums- you may be able to find a used Kuiu for under $300. If you can bump your price range up by $100 you may be able to find a used Kifaru, Exo, Stone Glacier or Mystery Ranch that will be a much better option and last you forever.
You all will get a kick out of this. I thought an expensive pack was like $200..........Yes, I almost swallowed my tongue when I saw the prices on the Exo's (first site I went to). Wow..... I realize it's an investment..But dang. I will be scouring the interwebs for a used one. Hard to drop that kind of cash on a pack when I'll likely not use but a couple times a year. And thanks for all of your helpful tips.
Never used one, but I have some friends who like the Kuiu packs. There are some in their outlet section for decent prices right now. If you look hard you might fine a used Stone Glacier krux frame in your budget now that they released a new frame.
There are two areas I concentrate on when it comes to gear. Packs and boots. I would definitely look at getting used in that price range and the ones people have spoke about are great choices. Find what fits and you'll never look back.
I bought an EXO 3500 2 years ago. It is definitely an investment, but I find that I use it all the time. I too upgraded from an Eberlestock, and assortment of REI and other non-hunting packs. The EXO (and I'm sure Kifarus and Stone Glaciers would be the same) just amazes me at what it can carry, and how comfortable it is. I use it to pack waders and fly fishing gear back into high alpine lakes or hard to get to streams. I use it to pack treestands deep into the woods, and now that my boy is starting bowhunting, packing 2 treestands is a breeze. I use it to pack a doublebull blind way back in for turkey or deer. I load it up for a week of backcountry elk or deer hunting. I have packed a mule deer out (Montana), and 3 whitetails (1 CO and 2 Nebraska) so far. But again, it is so much more than just a meat hauler. At somewhere just north of 4.5 lbs., it'll collapse down and makes for a good dack also.
+1 for the backpacking packs, if you are ok with it not being camouflaged. I was really disappointed in the camo packs I looked at in Sportsman's Warehouse - they are all twice as heavy and/or twice as expensive as some very good backpacking backpacks.