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One way to help solve the issue of getting the boys back into the cage would be to house one of your budgies on a separate cage.
If Decca isn't bonded with the pair you have adopted, then you can house him separately, this would also prevent any arguments between your budgies to escalate into vicious fighting once they come into breeding condition.
In case you don't know, it's not advisable to house an odd number of budgies especially when they are mix gendered, because the chances of fights to happen for the affection of the budgie of the opposite gender are much higher.
Your budgies would still be able to have out of cage time together and this way it would be easier make each of them to step up onto your finger or perch, carefully guide the budgie onto the cage, close the door and repeat the procedure with the other budgie.
You can also train your budgies to go back to their cages by using positive reinforcement techniques that reward good behaviour.
You can check this link for the detailed information: https://talkbudgies.com/taming-bondin...-training.html