Well since you're trying to stay within 300 buck range or less maybe the fixed 12X or 16X is your best compromise. Unless you can use a holdover Horus type reticle instead of dialing. Then maybe a Primary Arms 4-14X R Grid might work. But I have no idea how good the glass will be. Some like them, some hate them.
I would lean towards the 12x SWFA for the OP's intended purpose and budget. Mirage is definitely going to be an issue out past 800 yards, more often than not, even at 12x, particularly with the setup the OP described. 16x or 20x will only compound the issue. Running a 26" or longer barrel with high rate of sustained fire, is going to build a lot of heat right in front of his scope, even if he uses a cylinder contour. Unless he has enough discipline to substantially limit his rate of fire and runs a barrel shade on a shorter barrel than he initially proposed to use, or he uses additional rifle(s), he is going to experience issues with 16x or up scope. Also, his shooting position from a table/bench is fairly close to the ground with his targets being even closer. Throw in some higher ambient temperatures and 10+ mph winds, the combination of all these conditions is often going to cause some serious mirage dancing. If I were faced with a fixed power scope, I'd certainly sacrifice some magnification for lesser mirage shifting. I would even shorten my barrel to 24" maximum, and sacrifice the possibility of setting it back, just to help.
I believe the real answer is to first get a high quality variable scope in 4x to 6x low end magnification, that dials up to 20x to 24x at high end, and buy a decent buget sub-MOA guaranteed rifle to put it on, then build my dream rifle later, as funds became available. You may even be able to afford two rifles and put a SWFA fixed power scope on the second one! I've had excellent results from many Ruger American Predator rifles... I absolutely love my SWFA scopes, both fixed and variables.
Too bad I didn't see this post earlier. SWFA had a sale on two weeks ago for their SWFA SS 3-15x44mm scopes, with your choice of MOA-Quad or Mil-Quad reticle, $559.99 and a coupon for free S&H!