In my opinion, the sound of GM70 seems "grainy", a bit brutal and lacks sophistication. I have heard more than a dozen different amplifiers with the GM70 and they all have these characteristics. My friends experimented with drivers for GM70 and could not overcome these features. Unlike the 6?33?, the sound of which can be assembled like Lego.
I have only heard two GM70 SETs, Amplifon and the top model Lamm, neither of which sound anything like what you're describing, regardless of the specific type of GM70 (copper, graphite etc.) used. Quite on the contrary, those are amps that take the sound of the jumbo transmission tube family (211, 845, 805, GM70) to another level. I'd be curious what brands you're referring to.
Admittedly I've heard 845 amps that sound as you're describing, always ones with an output wattage over ca. 20 Watts Class A, later found out that this appears to be a result of overdriving them (attaching a link to the JAC Music article):
http://www.jacmusic.com/nos/GM70/
In a similar vein, I've heard 211 amps that sound strained (max 19.7 Watts Class A according to spec sheet), but not GM70 (max 43 Watts Class A according to spec sheet), quite on the contrary, I happen to find GM70 is one of my favorite sounding tubes, combining macro and micro dynamics with spot-on tonality. Having said that, same as 211, another of my favorites (on average a slightly more elegant, less lively sounding tube), a lot (if not everything) depends on the quality of the output transformer.
Greetings from Switzerland, David.