Domi has a very flexible slot layout, it can easily fit a shield or armor tank so it’s not an obvious problem. Loading up the low slots with damage mods and then shield tanking is viable. Or you can use the lows for armor tank and damage mods and use the mids for utility. Sounds like you have an XL shield booster and nothing to restore cap if it’s draining that fast. Typically on a mission ship you should only use an XL booster sometimes and stop boosting or cap inject if your cap goes below peak recharge (~25%). Don’t need to keep your shields at 100% all the time. I run a pithum c-type medium shield booster when I want something I can turn on and forget, with good resists and high damage it will hold.
At some point the Domi lost it’s hybrid damage bonus, but gained a drone range/tracking bonus, navy domi kept the dual damage bonus. Honestly I don’t really like either. With just drones the domi dps isn’t great, and with the dual weapon systems the navy domi has to sacrifice something to get good damage.
Gila is a very interesting cruiser, has a massive medium drone damage bonus, can fit a decent tank and since it is a cruiser as long as it has some speed it’s hard for mission npcs to hit it. The medium drones can largely shrug off aggro with the HP bonus, and will kill the frigs that target them quickly.
Ishtar is similar to the gila. Ishtar has a bit more flexibility in drones as it’s damage bonus applies to different sized drones, but is much smaller. Drone aggro mechanics may have changed since you last played, Ishtar will get good damage with heavy drones, but they will also likely take aggro. Ishtar could also drop sentry drones to snipe some of the small ships off the field early, but then you have to stay close to be able to scoop them if they take aggro, I usually just sit still or orbit at 1500m. Also it doesn’t do a lot of damage with sentries, although since the drones don’t need to fly off to their target they get a nice effective damage boost.
The best min/max for missions can be found here: