I would like to point out that I think that FS2-colour-style beams just don't look menacing enough for the Hades, IMO.
Besides which, do we even have a good reason for the blue / yellow / green colour of GTVA beams, beyond battlefield convention?
If the colour is itself the result of GTVA adaptation, then its possible that this is simply due to modifications as the technology was developed... it could be that the Hades had red beams which were more directly based on Shivan tech, but that as a result of both its destruction alongside the loss(?) of GTI intel, and that an inherent instability (overheating, power drain, requirement of a rare gas or alloy not found in sufficient quantities for fleet wide use) in the Hades beam tech made it unsuitable for widespread adoption.
Say, for example, that the Hades had to use recovered Shivan alloys in its construction to provide sufficiently strong power routing to its beam weapons - whilst you could get away with this for a single ship, its totally unfeasible for outfitting an entire fleet.
EDIT; also, having beams deliberately designed to look like Shivan / Lucifer ones would be a very effective psychological weapon.