Agggh.... Budgies!

Ok peeps
I need help here big time, regarding the budgies.

Everything seems to be going ok with the eggs so far. Mum is sitting in the nest box , dad brings her food and helps out in there so it's all good...

except...!!!!
He now keeps trying to escape the cage!

He's managed to squeeze his body through the bars twice now, and after flying around for a bit and sitting on the curtain pole etc, he then goes back into the cage (usually tempted by millet) But why is he doing this?

We've taken them outside into the garden before and he's never tried to get out of the cage.....We're terrified our cat will catch him if someone accidently leaves the door open and the moggie wanders in. He'd be killed for sure then.
Does anyone know if this is this normal behaviour in breeding birds? He's never done it before. Apart from netting , how can we stop him?

Looking for a smaller cage now BTW.
It's a terrible worry.