Then again, it might not have been the GTA that found out how to develop beam cannons--remember the Hades, anyone?

The Hades had Lucifer-style beam cannons implemented, though they were never used in Silent Threat. It is possible that, after examining either the wreckage of the Hades, or, more likely, by acquiring information from the GTI in one way or another, that the GTA and PVN learned how to better fit beam cannons into their own ships based off of the Hades' example.
The GTA didn't need to do all of the research into Shivan technology in order to acquire the beam tech--the GTI had already done that for them. It certainly was much more difficult than simply copy/pasting the Hades example (after all, it took a while before beam-equipped mainstream GTVA vessels started being produced), but it was possibly done through the GTI Rebellion in some way.