I BEAT SUPER-HAN!
Well, thanks to all your advice, I beat him the next time I played, which was today. I ran Trellix with HLC, Rebel Captive (one of my favorite cards) and APT (ended up not being used). I escorted him with 4 academy tie's.
And I attacked Han First. It honestly wasn't my plan, but he exposed and I could resist the zero defensive die. I blew him up on the 3rd turn. it was epic.
The swarm, plus the heavy hitter worked really well. I think next time I'm going to ditch the APT and get a seismic charge and a shield upgrade.
I'd go for an Engine Upgrade instead of a Shield Upgrade. Going from 10 to 11 hp isn't nearly as effective a boost as gaining, well, boost.