kid-kapowthat combo should be a killer setup for you, though I would opt for ATK Raider12 with Freeride spacers at your weight - same binding, just lower din settings, FR14s are meant for heavier riders than you as you would need to be at the lower limit or slightly below.
184s should be the obvious length given your weight and skill level.
Comparable skis would be Armada ARV 116 ultralights (softer option) or Whitewalkers (stiffer option - both 116 underfootm though the Whitewalker supposedly skis really similarly to BC120s, just like a slightly narrower version), ON3P Jeffrey118 tour or Moment Wildcat Tours - though you'll probably find BC120s at discounted prices more easily of the bunch.
To be fair, your description of the use they would see more or less sounds like an ad for BC120s intended use, so I would not over think it - they are supposedly great skis for the use you describe.
Raider12s are arguably the best hard charging, traditional tech bindings on the market imho. Build quality is fantastic, as is ride feel and release characteristics. Yes, they will have that somewhat harsh tech toe feel and they will not do your knees any favors (limited to no toe elasticity like all tech toes so all forces are transferred to your legs), but they ski as strong or stronger than the current crop of 600gr tech bindings (ion and rotation).
I would personally opt for Fritschi Vipecs instead (I have 100-150 days on Vipecs and Tectons, and a few on FR14s - so I am speaking from experience). They weigh a bit more at 600gr a foot compared to what 350?, but their toes are noticeably smoother due to their elasticity and the power transfer is better too (non rotating heel). No, you will not be able to feel much of a difference in untracked, deep, fresh snow, but more so on groomers or in variable snow.
Good call on the Fritschis for sure. If you want something a little safer for peace of mind OP, the Vipec or Tecton are super solid.
however, the Raider 12 is super reliable and out of the “minimalistic, freeride oriented” pin bindings, it’s best in class IMO. Freeride spacer would also be cool as it adds another connection to the ski, so you have the pins in front and rear with the spacer that enhances power transfer. Either binding would be dope on the BC120