It seems that Mjolnir are making a number of different amps - each one a Kevin Gilmore design? What is the difference between all the versions listed on his site?
All of the Mjolnir amps are designed by Kevin Gilmore, that's what the KG stands for.
The original electrostatic headphone solid state amp was the KGSS (Kevin Gilmore Solid State), designed in the 1990s - AFAIK nobody is building these anymore. At one point HeadAmp built them (they now build the Aristaeus and Blue Hawaii Special Edition).
An update of that was the KGSSHV (HV for high voltage) with improved third stage and higher voltage transistor output stage, and better PS in the full size versions.
The most recent all solid state design is the KGSS Carbon, using Silicon Carbide MOSFETS with a more linear output stage, more expensive than the KGSSHV, most advanced power supply in the full size versions. This is reportedly the best sounding and roughly the same level as the BHSE, although some regard it as the same level as the DIY T2. I haven't heard any of them other than the BHSE, and the number of persons that have compared them AND commented on the internet can probably be counted on the fingers of both hands.
The mini versions of the above use a more basic regulated power supply, which may cause some losses in dynamics and soundstage - how significant this is to you depends on your sensitivity to those difference. Note that the Stax amps all have a passive HV power supply (the more recent ones have a 7815/7915 IC regulated PS for the low voltage front end).
The KGST, as spritzer put it, is "a Stax SRM-007t made with no cost or retail considerations." It uses single (6S4A) vs double triode tubes (paralleled 6FQ7) which can take more voltage and power, and AFAIK his version uses the more basic regulated PS.
The Octave is an all tube amp that is a balanced upgrade of Gilmore's all triode stat amp. It's still a good design but doesn't have the ability to drive the more difficult headphones that the other KG designs have.
AFAIK, all the Mjolnir amps are made with balanced XLR inputs, so if you want to use RCA you'll have to get a RCA to XLR converter.