Have you ever even shot that distance before? If not, I wouldn't be complaining about the .223 being weak. If you really want to learn long range Marksmanship, get a .223/5.56 and practice till you can hit Sub MOA groups at 400+ yards without a bench rest, bipod or sling.
A $300 scope is just room for error. Unless you can find a used IOR/Weaver/Zeiss for that price, I would stick with a more expensive scope, or just using battle Iron Sights (on most battle rifles/assault rifles).
Also, you need to attend either an Appleseed Marksmanship clinic, or something from CMP, or just ge lucky and have a seasoned LR shooter work with you.
Long Range shooting is fun, but it takes practice, a knowledge base, and good equipment. You don't have to purchase thousands of dollars of equipment; you just need a decent firearm with decent sights/optics and plenty of ammo.