I also don't like missile reloading on the Doom, mostly cause it generates Flux and I need that for Phasing. The only missiles I even really want that system for (on other ships) are Pilums though, the rest either refire fast enough or get the job done fast enough that reloads aren't that neccesary.
Never really had a problem with missiles tracking my Doom though, just stick some PD in those 4 small energy turrets and phase out if something gets too close
As for other systems it could have, I don't feel like making up a new one right now so I'll just look at the existing things:
High Energy Focus would be a good fit, but I worry it might be too overpowered on this.
Flares aren't really all that needed if you stick PD in those turrets, IMO, but they would be a fairly safe option. And they are pretty good with cloak, as the Afflictor shows (I hate how limited their ammo is, by the way).
EMP Emitter is interesting, but that really seems like more of an "annoying frigate" system.
Maneuvering Jets/Burn Drive don't make sense now that Cloak gives a speed bonus already anyway.
Point Defense Drones (either, though I feel laser would fit best flavour-wise) could be fun if they cloak with you, but if they don't they look incredibly useless/fiddly to play with.
Sensor Drones, see previous.
Terminator Drone I haven't actually played with yet, but on paper it looks like a good fit! Would it be balanced to have a rebuildable buddy on a ship without CR deterioration, though?
Ammo Feeder would really nullify the universality of those small hardpoints. It would fit a strike cruiser, but I don't like it on a high-tech ship like the Doom.
Phase Skimmer/Teleport? More Phasing is cool! Would probably make it a little too maneuverable for a cruiser (isn't already the fastest one?), but I could see an argument for Skimmer if the top speed was nerfed a little (which would conveniently make the Aurora the fastest again, if you don't look at the Falcon cause it's Light).
Fortress Shield, not to leave it out: uh. Maybe if it gives it a shield?
All in all, my vote's for the Terminator Drone or Phase Skimmer. They both also work nicely with the Doom being a wonder of Phase engineering!