One needs to realize that "flat shooting" is a relative term. At 1000 yards, there really is nothing that is flat shooting, you will either need to dial up for each shot or you will need to use a ballistic reticle for hold over at ranges past 500 yards and out.
One should also consider that the more intense the chambering the more it will be effected by temp changes and elevation changes. You have have the baddest beast on the planet but if its not consistant you will not kill many dogs.
The challange is hitting a target that is relatively small at very long ranges. My 7mm AM will certainly dump any yote at any range you can hit him at but I am not sure its the best choice for your application, YET...
How many rounds will you be putting through this rifle every year?
Since the Wildcat bullets are not available at the moment because the company is in the process of being sold, it takes a bit of smoke out of the 7mm AM fire. Its still the fastest out there but the main problem is its velocity and the next best commerically available high BC bullets such as the 180 gr Berger VLD.
The 7mm AM will hit 3400 fps easily with this bullet weight, only problem is that of all the rifles I have built and tested, the 180 gr berger does not care for velocity much over 3250 fps. This is a relatively mild load in the 7mm AM, in fact very mild.
If I am using a lighter bullet then the 200 gr ULD in the 7mm AM, it will be a 160 gr Accubond and I will load it to the nuts so to speak to flat out HORSEPOWER it out to long range. This goes against my theory of long range hunting but it will work. a 160 gr AB at 3500 fps is nothing to sneeze at. Still ballistically, the wind will infuence this bullet quite a bit at 1K, even when launched at 3500 fps.
You may want to consider something like a 7mm RUM loaded with the 180 gr Berger. This would allow you to use upper pressure loads for good consistant, clean powder burns and you would be right in the perfect velocity range for this bullet, 3100-3200 fps depending on barrel length.
May be a better choice for your application.
Let us know how many rounds you will be throwing down range every year and that will help alot.
One question I have, if your calling in yotes, why do you need a 1K rifle? You must have some seriously call shy yotes in your area. Generally in my area, they will hold up from 300-500 yards out if they are going to. In that case, there are any number of hot rifles that would serve your needs extremely well. The 257 STW comes to mind.