Autopulses are really excellent on the Paragon because it recharges while in fortress shield mode. The effective DPS stays close to its theoretical maximum, while for continuous firing weapons they lose out anytime the system is activated (or vents, or is out of range). The 4 Autopulse Paragon we saw later though had a lack of anti-armor, and turetted autopulse wastes a lot of shots - the earlier winner Paragon is a pretty good build, I like 2 tachs, 2 autopulse in hardpoints.
Regarding variations of the default eagle (3 Heavy Mortar, 3 Graviton): its not a terrible ship for AI hands, and I was pleasantly surprised by it when I did a default variant runthrough of forlorn hope. There aren't that many ships that can fire back effectively while under 600*shields additional flux, and the mortars are good enough HE to keep shields up. And its OP/flux cheap. I have my own favorite eagle build, but I've been thinking of giving this one a try more, or trying to find tweaks. The main issue is that kinetics + 1 ion beam is really, really good for lockdowns.
HILs are devastating weapons if they get through the shield. Compared to a Hephestus: the HIL has roughly the same DPS (500 vs 480), the same efficiency, and slightly more than double the armor penetration (500 vs 240). This is at the cost of soft flux instead of hard. As a specialist anti-armor/anti-hull weapon, very little can match it (tach lance does pretty god but is lower dps), and its a commonly found weapon. But its a specialist weapon: don't use it unless you can generate the situation where its amazing.