Thanks for the opportunity to take a look at these fairly new instruments which I was not aware of. I have limited experience with the reflectivity meters, but I have read a good deal about them (I’m a GIA trained gemologist and a long time gem cutter). The problem with them is that they can be unreliable if the gem is dirty or the polish is not so good. While they might work pretty well for many separations (e.g., is it diamond or colorless topaz?) they might not be able to differentiate between some gems whose reflectivity is close. They just don’t measure refractive index to two places like a refractometer does and you wouldn’t get any indication from the meter that it was “seeing” poor polish, whereas I can often get a refractometer reading off a rough stone’s crystal face or cleavage plane and if the polish isn’t good enough or the surface isn’t flat enough, I can see that my shadow edge or rainbow is dim or non-existent and I know the instrument isn’t working. Also, if you learn how to use it well, the refractometer will give you a measurement of birefringence, if any, and can also measure optic character and optic sign. Lots more info to confirm any possible ID. The problem is that you have to learn some gemology to use the refractometer well.
IDK much about the thermal conductivity meters for colored stones. They work pretty well for separating diamonds from any other simulants except moissanite, and anyone with a little knowledge can see the doubled facets on the back of a moissanite with a 10X loupe. Elsewise buy the more expensive tester that tests for moissanite. For colored stones, there are some whose conductivity is close to that of another, so you could end up with IDs that are questionable, I think. How sure do you want to be that your ID is correct? I don’t know whether these instruments are reliable or not and I haven’t seen more than a few reviews on ebay, none elsewhere. These are more expensive than a refractometer, about $250, whereas the cheap Chinese refractometer would be about $95 on ebay with a light source and RI fluid included. These are workable instruments, you just need to check the RI against some quartz, which is pretty invariant, and be able to return/exchange it if the calibration (which is non-adjustable) is off, which sometimes occurs. Since some stones are “over the limit” of the refractometer, you could supplement it with a simple thermal conductivity diamond tester costing about $15 or less.
If you wanted to learn a little more gemology, you could start screening for the separations you mentioned with a simple specific gravity measurement using a $15 digital scale plus a very small plastic cup for water, but this would only work on loose gems and you have to learn how to do it (not that hard). Other simple gem instruments that might be helpful are a polariscope ($20), a dichroscope ($20), or a set of Hanneman filters. Some of the filters DO help you distinguish various blue gems from one another, synthetic from natural emerald, etc. Instructions come with the filters, while a book like A. Matlins Gem Identification Made Easy would help with the polariscope and dichroscope and also the refractometer.
None of these methods is going to help you at all to distinguish between synthetics and natural gems and most of those separations have to be made by using magnification to look at internal characteristics of the stones and comparing them to on line or in book photos of inclusions.
I know this is a lot of info, but gemology questions often don’t have simple answers. If someone knowledgeable has info on how the new thermal conductivity testers work on colored stones, I’m all ears.