Well, your sitation presents some problems, but nothing that can't be worked through. Kudos to you
for trying to keep the Meezer from the shelter!
How about setting up a semi-private super-large dog crate?
This would be sort of stepping-up the intro process a bit by eliminating the behind-closed-doors step and going right to visual with partial access. If you use Feliway, Composure Liquid and/or Rescue Remedy it may help this accelerated step go smoother...
I have a wire crate that is 3x5x4tall that I use outside for holding stray dogs or letting kitties sit outside to enjoy fresh air while we are with them on the patio. This year I want to make some sturdy shelves to put in it so I can let several kitties be in it at the same time and not feel too crowded with only the floor to share.
If you place this in a corner of the room so the new kitty has two sides and a corner she can safely retreat to and be completely hidden from Mochi, but also with shelves so new kitty can get up 'high' and feel safer and more confident, this will allow them to be in the same living space and interact in a partial manner. I would also place Mochi in your room for periods of time to allow the new kitty out to explore, exercise, spread her scent through the home and spend quality bonding-time with her new family.
That's all the ideas I've got...