Basically, as long as you can get the AC tubes inside the firewall (which you should be able to based on your description) and pull the assembly down, you'll be able to remove the heater core lid as I described through the glove box opening and and then the core itself.
The evaporator housing might make getting the lid/core out a tad more difficult, but it'll come. Will just take some additional fighting/swearing
Had to see but yeah, I think that'll go inside the car no problem. That's the reason you need to loosen the dash frame on the side, so that it gives you enough space to pull the tubes inside the car and let the assembly slide down toward the passenger side floorpan.