Why do you care if your heart rate gets out of zone 2? The idea is to improve your speed not keep your HR low. If your HR gets too high use a lower gear.
No. The idea is to keep the HR low. Otherwise it becomes a different workout. It's easy to increase speed if you don't care what your HR is. The trick is to pedal as high a cadence as possible while staying in zone 2. I usually only manage about 117.
So, thoughts. Of course reduce your gear, but I'm assuming you're already in the easiest gear you care to use. If your gear is too low, rim momentum gets too low and the drill becomes even harder in a way.
Keep your back straight. Hold the bar tops. Relax your shoulders. Drop your shoulder blades. For high cadence drills, keep your feet flat - don't ankle. Relax your toes. Pedal as though there were a cushion of air between your foot and the shoe sole, all the way around the circle.
For OLP, pedal heels down but drop your toe after the end of the bottom stroke. Don't do OLP at over 85 cadence. You can cause problems, and there's no reason to do it. You are trying to improve your seated climbing power. Use enough gear that you are crying for your mama at the end of each interval. Because you only use one leg, your HR should stay low no matter how hard you work. If your HR gets too high, do longer intervals! Yes! Later intervals will be easier than earlier ones. Suffer through.
Those things said and tried, just do what RPM you can and stay in zone. It will gradually increase with practice. Practice creates efficiency, which is mostly neuromuscular coordination. It could take a year or two to plateau with these exercises.