Really. Just give up running entirely.
Burnout and mental fatigue almost always kick in when humans overdo a particular activity. Put another way: If you do something too frequently, you'll simply get bored with it, no matter if you're a casual jogger or an elite long-distance runner.
As evidence, take a look at Kilian Jornet, who grew up on a mountain in the Catalonian Pyrenees. At only 24 years old, he's already a three-time winner of the Ultra-Trail du Mont-Blanc, a 103-mile (166 km) event that's considered the hardest footrace in Europe.
Although it might seem odd, Jornet doesn't define himself as a runner. Instead, he consistently tells interviewers that he is a mountaineer. He loves all mountain-based activities, from hiking, to skiing, and of course, trail running. And from October to April when running races are rare, he switches entirely to skiing, which keeps him in top physical condition until spring. The change of pace prevents him from developing overuse injuries and refreshes him mentally and emotionally, too.
The point here is that you don't have to doggedly stick to running a certain number of times per week, especially if you find those runs agonizing or just boring. Follow your passion and focus on what's important, which is keeping your body in shape to the benefit of your mental and physical health. You may find that you like cycling exclusively for a few months out of the year, and then decide that you dearly miss running, at which time you can fully embrace the fun and excitement of hitting your favorite trail once again.