I just read the OP again. Yeah, man. These guys recommending the top-tier stuff are not taking your budget for gun AND SCOPE into account. You can cross the KAC SR25 and HK MR762 off of your list as you're not going to be able to put a reasonable scope on them and remain within your budget. Without some sort of discount, the KAC is going to exceed your budget before you buy any accessories.
The LMT MWS *might* be barely possible if you can get good pricing on them in the old sub-$2,500 range, but at the moment I think you may end up $3k+ range. If you go for a decent mid-tier LPVO like a Vortex Razor HD Gen 2, then you're at ~$1,300 for the scope. Add on some taxes and shipping and you'll hit your cap pretty fast. Hopefully, you're already G2G on Mags, ammo, a sling, other accessories and already like what comes directly on the gun without need for customization.
So, with that in mind, you could pull off a top-tier rifle in the LMT. Alternatively, you could start with the Aero for $1,100-1,300, add the optic, and have ~$2,500 in it to start with, and then mod/accessorize to customize your rifle to your liking. I just recently did both. I looked at/held/shot Savage, M&P, DPMS, Sig, Ruger etc... I was impressed with several, and I especially appreciate the weight-reducing direction designs are headed these days, but when I started reading about the difficulties with parts and long-term factory support for proprietary designs, I decided to steer clear and stick with something that lends itself to easy part replacement across many manufacturers. When the entire industry supports your choice, you can keep your rifle forever. Plus, when you start research each one, you'll find things to knit-pick & consumer issues/common problems. Aero isn't the only non-proprietary game in town but I don't think you can do better in the quality/$ game. I think they're a mid-upper tier manufacturer for low-budget prices.
My answer was to go with both Aero & KAC, but I could have flipped a coin and gone with the LMT instead of the KAC.