I think it would be really cool if you could search over all decks with the Ankiweb search.
Is there a way for me to help you to get this done?
The way shared decks are currently handled does not make this practical, sorry.
OK. This will mean I will leave as soon as I found a better alternative.
The better alternative is Anki Desktop. But if you have to use Ankiweb, you could just add a common parent deck.