Started a new run with the latest version (v1.8 ), and am happy to report that superweapons are actually dropping from stations/caches now. I've explored ~60% of the sector, and so far have found one BFG and one phalanx, which IMO is a sensible enough drop rate. Thanks for listening to the feedback!
Speaking of feedback: instead of the current implementation, how about having the BFG AOE be a damaging plasma cloud that persists for a while after the projectile connects or reaches max range? The BFG projectile already looks like a gargantuan ball of green superheated plasma, so this kinda fits its image already -- I imagine that much energy will still be dangerous even after it connects.
The reason I thought of this: after trying it for a few large-ish (>250) fleet battles, I swapped the BFG out for the phalanx and didn't look back. Yes, it's powerful (~5x the raw damage of each phalanx shot), but that's all it has going for it. Unmodded, the BFG shot is quite slow, so it can be avoided even by sufficiently nimble cruisers. The AOE effect doesn't feel that good either, as it's usually too weak to affect shielded cruisers much, and most frigates can exit the AOE quickly enough to minimize damage. The 30s cooldown also makes every missed shot that much more painful. But even if you connect, since the AOE effect disappears with the projectile, most of the time the BFG shot just gets used to overload enemy shields, after which you need to use other weapons -- or other ships -- to exploit that overload. (phalanx solves this by being a two-shot -- if the first one pops the shield, the second impacts hull, so you exploit without having to wait for the cooldown or depend on other weapons.)
I tried to mitigate some of these weaknesses by using hullmods that boost projectile speed, but that's also a double-edged sword: it helps with hit rate, but since the projectile moves faster it makes the current AOE far less useful as enemies stay in the AOE for far less time.