You've convinced yourself that you need a better gun. Is it also possible that when you get those longer shots, you may have convinced yourself you're going to miss? What people like to call "buck fever" is a sort of self-deprecating mental thing we're all prone to on occasion. The pressure not to fail turns into a weird, self-fulfilling prophecy. There's a cure. If you can so easily convince yourself that your equipment is substandard, you can just as easily convince yourself that there is no pressure to either hit or miss your target.
An 80-acre plot of ground, after the crops are harvested, is my favorite place to practice the fine art of mental preparation. I pick a spot in the middle somewhere, and set out a bunch of 5-gallon, white buckets with numbers painted on them. I set stuffed animals from thrift stores on them. Ranges from 60 yards to 350 yards. I go back to my chosen shooting spot and have the wife call out numbers, and begin the slaughter. When I've killed them all, I move the shooting spot back about 100 yards, range the buckets again, and start it all over. Great for getting kids/grandkids used to shooting at various ranges, too.
The stuffed animals don't need to be realistic. The goofier they are, the better. My favorites have been a quite large Barney the Purple Dinosaur and a really big Ronald McDonald. I'm afraid to admit how much pleasure I've gotten from assasinating poor, headless Ronald.
Next coyote hunt, when you see one out there at 325 yards, tell yourself, "Sorry, Ronald, but you're poisoning my kids with your greasy food!" and BLAM! take that clown out with a head shot. The trick is simple... stuffed toys won't run off or bleed or laugh at you for missing. Treat the critter like a stuffed toy until that missing problem goes away.
This might win me an award for goofiest reply in a predator hunting forum, but hey... if you have a blast doing it, and it teaches you to relax and just shoot... who cares how goofy it sounds, right?