What a great Mothers Day present! And watch those budgie numbers, they climb without you even realising it!
Budgies are funny little things, the majority of my budgies sleep on the wire too. I used to have them in an aviary that sounds similar to what you've described, though now they're in one with one solid side, one sheltered side, and two open sides. They are happy to sleep on the sheltered side now, but in the other aviary they would always hang on the wire.
My belief is that they like the airflow. It's not really natural for budgies to be completely out of the weather. One thing I used to do was hang folded shadecloth down the open side of the aviary, pulling it aside during the day and covering it at night. It helps keep the worst of the weather out, and hides them from potential nocturnal predators.
As for not sitting on the purchases, my belief is they prefer to be as high as possible. My birds sit right up on the wire near the roof, which is the highest they can go and which, in the wild, would get them as far from predators as possible.
You could try putting some little perches high in the back corner of the aviary, and perhaps they might use them.
You know you might have too many budgies when you're not sure if you've remembered them all!
Charlie - Cinny - Dante - Gidget - Jimmette - JJ - Jules - Mo - Ollie - Peanut - Penny - Pie - PJ - Pockie - Sally - Simon - Snowy - Song - Sora - Spang - Tommy