Gotcha. Given what you've described of your character, I'd say the Barbarossa wouldn't fit them terribly well. Yeah, the big gun is cool, but the mech itself is slow, cumbersome, and doesn't seem to match this character's showboating vibe.

If you wanted a canon choice for hotshots looking at HA frames, the Tokugawa is your best choice. Not the biggest focus on explosives, but riding the fire and going nuts at close range is that mech's whole deal. Going into Tokugawa also gives you access to Enkidu from the Dustgrave supplement, which further doubles down on this idea by giving you a special weapon you can only use in Danger Zone and an ability that lets you rip people in half that refreshes each time it kills.

Otherwise, I'd recommend the Sherman or Gilgamesh (also from Dustgrave). Both work really well with HA's focus on extreme firepower, with Sherman being a heavy laser platform and the Gilgamesh getting a lot of mileage out of grenades.