Four months is a bit on the late side to get a non-tame bird tame. Especially when you have two. They tend to bond more with eachother than with their owner. But seeing they dont freak out when you go into the cage you have a nice base to start from.
I wouldnt seperate them, that would just cause extra stress. I woulndt advise you to take a 2 week break either. They wil just get wilder and wilder.
Do what you do now. Go into the cage, offer food, try to get closer to them. If the freak out, you go to fast. Take a step back and start again. In time you will become failiar enough for them to take food from you and to step up. But it could take a long time for birds that arent used to human contact.
Try to keep the traing sessions (this desensitizing is training too!) not too long. 5 to 10 min max and multiple times a day. Try to end on a positive note. Dont end the session when one of them freaks out. That will teach them that you will leave them alone if the freak out.
This topic answers a lot of your questions and gives a good guideline to follow:
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