The GES is based on Kevin Gilmore's all triode amp, which was one of his first designs. When he designed his KGSS, he felt it sounded better (with the SR-007 Mk I, which was the top of the line at the time) than his all triode amp. The KGSSHV and KGSS Carbon are advances on the original KGSS. The problem with the GES and the Stax tube output amps is they all use plate resistor outputs. All the Stax solid state amps and all the modern Gilmore amps including the KGST use current source loads, which more than doubles the effective output power of the amp because they are not wasting the majority of their power heating up the output resistors. In fact, just taking the SRM-T1, which is basically the same circuit as the 006 and 007, and replacing the output resistors with good cascode MOSFET current loads kicks it up to being able to drive the SR-007 adequately for most people. The modified T1 is essentially a lower power version of the KGST (6CG7 rather than 6S4A output tubes), but lacking the regulated power supply of the KGST.
IMHO, a modified T1 is the least expensive way to get an amp that will drive any Stax headphone - the cost is basically that of a used T1, plus another $100 in parts, which includes the cost of replacing all the power supply electrolytic capacitors, which needs to be done in an amp that is more than 25 years old anyway. If you don't want to DIY, any repair technician should be able to do the modification with a few hours work. If you already have an SRM-007, modifying it with current sources in place of its plate resistors will significantly improve its bass and high end, along with its ability to drive the 007.
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@antimatter, I feel an SRM-727 with global feedback mod is capable of driving the SR-007, although I prefer the sound of a modified T1 - I had both, and sold the modified 727.
As I have mentioned elsewhere, an SRX Plus is also a reasonably inexpensive amplifier that will drive any Stax headphone, however it is a DIY only design. It does have that tube tonality with very little of the stereotypical tube defects of soft bass and highs.
Using the Stereophile ranking system, the SRX Plus would fit in class B along with the KGSSHV and KGST, while consensus class A amps would be the Carbon, BHSE, GG and Megatron, with many placing the T2 in class A+.
There are a couple people (e.g. spritzer) who would put the T2 in class A with the other KG amps, and a few people who would rank the SRX Plus in the same category as the BHSE, but what I have written in the previous paragraph is what seems the most prevalent opinion.
Finally, it should be noted that with amps which are predominantly DIY, there may be small differences due to parts selection, and differences due to choice of regulated power supplies. Kevin Gilmore has designed several regulated power supplies of varying complexity and performance. KGSS Carbons often are built with his most sophisticated Golden Reference supplies, whereas the less costly KGSSHV and KGST are more commonly built with one of his lesser supplies, which may enhance the differences in performance between, say, a small KGST with a simple regulated supply versus a large KGSS Carbon with Golden Reference HV and LV regulated supplies.