Confirm my diagnosis!

I've seen smoke coming from my vents on very humid days. Many a time.

I could see why you think heater core, but that isn't the only scenario that produces the smoke in vents.

Another is when it's 100+(Texas) and you turn the AC on. When it's real bright in car from sun, the smoke is there. No wet carpet?

And the coolant won't rise in the overflow everytime.
I had smoke coming out of vents and light coolant drip out of the ac drain tube on engine bay firewall. My understanding is that if coolant ever comes out of there, your heater core is cooked.