I have used the Galaxy Audio GalaxyTrek GT-S Portable Wireless Headset Microphone, available on Amazon for $89.99 (quite possibly the unit you were looking at). It delivers great sound fidelity and lasts well over four hours on a charge. The pickup is very directional, which gives it good noise and feedback rejection. However, I have had problems with it cutting in and out sometimes, even when standing close to the receiver. I assume this is due to interference; we dance in a studio with a million bluetooth-controlled party lights, about a dozen fans, a bluetooth audio system, and a neighboring theater with probably at least as much going on. Turning the headset off and on fixes it for a bit, but interrupts me for about 10 seconds. A few minutes later, it's cutting again. I assume that power cycling makes it select a different frequency. There is no manual frequency control. The gooseneck is just a little short for me. In order to get it right in front of my mouth, the foam cushion is sometimes touching my lips, which I find gross.
So, I bought a headset with a battery pack, the Monoprice Instrument Dynamic Microphone Black (600060), available on Amazon for $120.28. I know you don't want a battery pack, but this unit was recommended on another Shared Weight list, so I'll review it here. Range and sound quality were both excellent, and it cures the cutting problem of the GalaxyTrek. It shows you the frequency and you can control that manually (but don't have to; it's never cut for me). And, you get two mics, which go out either joint or separate channels on the back of the receiver. But, the pickup is much less directional, and we've had feedback problems with the unit when the band plays very loud, despite our excellent sound guy's best efforts. Again, the gooseneck is a little short, though the lower directionality makes this less of an issue.
Perhaps these Chinese-made units were tested on smaller heads? I know I've got an ego, but...