It's important to remember that when you're comparing a given launching platform, like the WSM case, you'll always get less wind drift with a 7mm vs. a .300. This is simple math. Compare the BC values of the most aerodynamic bullets in each caliber. The .300 has the 208gr A-Max, 210gr VLD, and recently the 215 and 230gr Target Hybrids were also introduced. The 7mm has the 162gr A-Max, 168gr VLD, 180gr VLD, and 180gr Target Hybrid (of course you've also got the 180gr JLK, but then your costs go up).
Bryan Litz did an article about the 7mm 180gr Hybrid, and mentioned that it's BC is lower than it should be because Berger used a wider meplate on this bullet than on most other bullets. This increased the uniformity of the tip in production, but decreased the BC. Bryan mentions that a quick pointing of the tip results in an enormous 8% increase in BC, where pointing most bullets results in a 2-4% increase because of the already narrow meplat of most Hybrid and VLD bullets. If you add 8% to the BC of the 180gr 7mm Hybrid, you'll see that it's slightly better than the BC of the 230gr .308 Hybrid. Here is a quote from Bryan:
"The special secret of this bullet is that since it has a wider than average meplat, the drag reduction that’s possible from aftermarket pointing of the meplat is much more than average. Typically the drag can be reduced (BC increased) by 2-4% for most bullets that already have small meplats. However, since the meplat of the hybrid is so wide to begin with, it’s BC is increased by 8% when pointed! This is a substantial improvement which is evident in the ballistic performance and puts this bullet head and shoulders above anything else under .338 caliber for ballistic performance."
In any case, In order to match the BC of the 7mm pills, you need a much heavier .308 bullet, which means that the case in question (in this case it's the WSM) won't be able to push it as fast. The 162gr A-Max has a 0.625 G1 BC, for example, and in order to match that, you need to go to the 208gr A-Max in .308", which has a G1 BC of 0.648. You can launch the 162gr A-Max to 3100+fps from the WSM case, but you'd be lucky to get 2950fps from the 208gr A-Max from the same case. If you compute the wind drift charts for both loads, they nearly duplicate each other, with the 7mm having the slight advantage past 1000 yards by a measly couple of inches. In the case of coyotes, there is absolutely no reason to go with the larger caliber, unless you're willing to burn a lot more powder and spend more on bullets.
For the OP's application, I would go with something in 6.5, and would likely just build a .260 or .260AI. If you want a truly cost-effective alternative, I would build a .243AI and load the 105gr Hornady HPBT, or a 115gr option. It's pretty hard to find a more effective solution that costs less to load. The .260AI may be the best compromise, here, if you're hoping to get out to 1500+ yards. I know a fella that hammers more coyotes than anybody else I've ever known, and his choices for coyotes out to a mile are the 6XC and the .260 (his longest shot on a coyote is just shy of a mile, and was made with the 6XC).