It's just not that simple. Yes, anything over 100bpm is generally considered sinus tachycardia, however sinus tachycardia itself has dozens of causes, anything from exercise and anxiety to serious medical conditions. And you don't treat "sinus tachycardia", you have to treat the underlying condition. In a case like mine, and possibly yours, there's just nothing that can be done, or at least nothing that is very well clinically studied and proven. I've read that a combination of an SSRI plus something like buproprion or mirtazepine can help "reset" the autonomic nervous system over a period of weeks/months, but this doesn't appear to have been well studied. I might give it a shot at some point, just for the hell of it.
In any event, it's important to remember that 100bpm was chosen somewhat arbitrarily as the limit after which the heart rate would be deemed tachycardia. It's not as if your health is guaranteed if your heart rate is 100bpm, and you're doomed to die early if it's 101bpm. It depends greatly on whether you have any structural or conduction abnormalities in the heart which are comorbid with the tachycardia, and what your blood pressure is. I've had a full heart workup including an echocardiogram, cardiac event monitor, and so on. So I can feel fairly confident I'm not going to drop dead from tachycardia anytime soon. I do have to have another echocardiogram in another 4-5 years, just to ensure that no damage is occurring to the heart valves.
But like I was saying before, while you can't treat hypertension from stimulants from beta blockers, if you have tachycardia without hypertension, then beta blockers may be beneficial. Yes, they raise blood pressure, but that's kind of the point. As long as you're not getting into the hypertension range, then an increase in blood pressure can be beneficial and actually slow the heart rate further. Look up Postural Orthostatic Tachycardia Syndrome (POTS) -- This is a type of dysautonomia which involves a large increase in heart rate upon standing, similar to what happens to me. The primary treatments are in fact beta blockers and vasopressors to reduce heart rate and increase blood pressure. Note that I'm only using POTS as an example, the treatment here may not apply to your particular situation at all, depending on what the specific underlying condition you have is.
Either way, you should definitely be working to either resolve your heart issues so you can endure the stimulants, or trial non-stimulant medications and see if you can get a better benefit from something else. Maybe you won't be able to deal with stimulants, but could handle one or more of Remeron, Wellbutrin, and Xyrem. Even seeing a moderate improvement would be better than feeling like crap all the time, I would imagine. I will say it's strange you can handle caffeine but not stimulants. Caffeine usually has a greater effect on the heart than amphetamines or the non-stimulant wakefulness promoting drugs do.