Shy bird introductions and Housing question

[LoveMyConlan]

My 4 month old female Sun Conure, Mouse, is very shy of other birds. She was by herself at the caregivers, her only interaction being from a distance, but is great with people. My female GCC, Conlan who is 8 months old, has been by herself for 4 months. When we did basic introductions in a neutral space Conlan we preening Mouse and being slow about movements, very sweet. Poor Mouse was just at a loss at what to do. She wasn't afraid, just sat there ignoring her with her for tucked up, but when Conlan would preen her, she'd squeek and flip her wing. Conlan of course stopped.
I would eventually like to place them together but how do I make Mouse more comfortable without it causing one trying to become dominant?

Question 2. I finally located my Turquoise GCC from a breeder and will be bringing HIM home in October. Can I have him in the same Room as my girls? He won't be allowed anywhere near them. Ever. No babies here!!

 

[Doublete]

Wait, by place them together what do you mean? Not same cage?
I wouldn't recommend that at all.

 

[LoveMyConlan]

Wait, by place them together what do you mean? Not same cage?
I wouldn't recommend that at all.

That was ultimately the goal. I know it's going to take a LONG while before then. Both are female and neither show dominant behavior with one another. They have been side by side in separate cages, about 6 inches apart (they were a foot), for a while and will sit against the bars 'next' to one another. We've had then out at the same time just on different couches and over the 2 weeks got closer. Last night was the first time they both day on my hands together.

 

[Doublete]

I always look at it this way...
Would you like to be stuck in a jail cell 24/7 essentially with another person?
I wouldn't house animals in the same cage because they don't have an option to open their cage and have a few moments to themselves.
Just my opinion I guess.