The ship isn't going to be inaccessible to normal sized people. You said yourself have a crew from somewhere else do repairs. Well that crew has to be able to move around inside, otherwise they can't do internal repairs or engine maintenance or any of that. So yes, such a ship would be boardable, simply because if it's not, it becomes a logistical nightmare in terms or maintenance.
Like I said size does not proportionally scale to performance even in the real world, you could make an engine 50% large and only get a 10% boost to power. Even if you're directly stacking reactors, that doesn't mean you get the full benefit of them all. Other systems and energy pathways will be a bottle neck, and will limit the capabilities. Yeah you'll be less likely to have total failure because you have to have each reactor fail, but having twice the reactors does not guarantee twice the performance. In order to do that everything attache dot the reactors has to upgrade as well. Engines have a max output, the energy relays have max outputs, inertia dampeners have limits, the ship's physical structure has limits, all of this would bottle neck the increase in performance.
And engineer's do repairs on systems and equipment mid battle. They aren't repairing the physical structure a lot, but of conduits blow out, or parts fail, they're not just gonna twiddle their thumbs and watch, they're going to try to get the ship back in best operational condition as soon as possible. Like you yourself said think about it -logically-. If you lose you -die-. You're going to do everything in your power to make sure the ship doesn't sink. If that means performing repairs on an active reactor in the middle of a fight, then that's just what you gotta do.
The reason why an exploration ship is a better idea for this is because simply put it is less likely to encounter situations that bring up the Mini neko's natural disadvantage. This is because most of the time a exploration ship is moving at its own pace. Yes they will sometimes get into fights and sometime other things will happen. But most of the time is spent doing things its own way. Where as a combat ship is forced to operate in situations dictated by external factors and many times it can't just go "Well I'm not good at this, I'm just gonna leave."