I purchased my first hive last Spring ('05 - Italians) and they did really well last year. Both hive bodies are full of brood and honey.
... The hive is really strong and everything seems to be in order in both the hive bodies. .
You live quite in south and summer is going on your place. We have just now the start of apple blossom.
To me 2 box hive is really small. My hives overwintered in 2 or one hive box. To 2-box winterer I should now add fourth deep. They have 2 box full of brood.
If hive is full of bees and it need not your third box, it seem that you have not much honey in nature.
I cannot say nothing else but get a new queen and look what happens then. Or you split hive into two and get two queens.
If queen is several years old it is not able lay eggs any more. I change my queens every year.