I'm going to blame your thermometers.
The one you used for your first batch you believe was a bad one, so it likely was measuring the temperature incorrectly, so you got poor results.
Then, you bought a really fancy infrared thermometer... which is great for measuring surface temperature but is pretty useless for anything else. Note that surface temp is usually much different than internal temp. Generally, if you're heating something up, the surface will be hotter than the inside and if you're cooling something down, the surface will be cooler than the inside.
This means that all your temperature readings were wrong!
Here's some info about the internal temperature reading myth:
2. An infrared thermometer will tell you the internal temperature
This is another myth worth busting. An infrared thermometer is a surface temperature tool – period. If you’re grilling, baking, smoking, or roasting you’re going to need a penetration probe to tell you the internal temperature of the food you’re cooking. An infrared will only give you the surface temperature of the food, and depending on your optical range, the temp of the surrounding grill, skillet, oven, etc.
I think you should try your chocolate tempering again but with a good-quality instant read thermometer (make sure the temperature range goes low enough) or a candy thermometer (again, some of them start at 100 F, so make sure it goes to the temps you need).
It seems that everything went well and your chocolate is tempered after all.
High quality chocolate has no other fat but cocoa butter, and couverture has much more cocoa butter than a chocolate bar. This is what it gives it the "snappy" feeling when bitten, and what makes it melt in the mouth (and in your fingers) instantly. The cocoa butter in tempered chocolate has a melting point of about 32 Celsius, 5 degrees lower than the human body, and you can't hold it in your fingers for long.
If you don't want this to happen, you will have to use something else. Cheap baking chocolate should be a good substitute - it also has a very high fat content, but it uses vegetable fat, not cocoa butter, and it is harder and less melty. Bar chocolate can work as well, but depending on which one you choose it will either have too much non-fat solids, or added fat of the wrong (soft) type. Depending on where you live, it can also be waxy - that is common for example in the USA.
Distempered chocolate is grainy, sandy, and has bloom (a dirty white powdery covering). As long as you don't have them, your chocolate is fine, no matter which kind you took.
Best Answer
The way you've described is precisely how I melt chocolate. If you have a double boiler, that's even better, but a bowl on top of a pot is fine too.
I can only think of two things that might be affecting the quality of your end result:
Is the bowl big enough? The melting bowl should be larger than the pot if possible; you want the steam to be forced under and around it.
Is the water temperature reasonable? You want it to be at a simmer. If it's rapidly boiling, the heat is too high.
As long as you keep those two things in mind, your chocolate should melt fine!
Edit: Thought of one other thing: