How to do address autocomplete right?

I'm working on a webshop that wants to introduct automatic address completion using googles Place Automcomplete API. My main focus is usability and getting it right isn't exactly easy. My main problems are:

• the browsers autofill-function overlays most "classic" approaches that just show googles suggestions right below the input field. Disabling autofill for the field would be the easiest approach, but I don't want that either. Users that have the right address in their autofill should be able to use it, but those who don't should be able to use Googles suggestions. From a UI standpoint I dont want anything to overlay anything - so that's my first problem: Where/How to display Googles suggestions? I was thinking about putting it into a speech bubble above the field, but users aren't used to that.

• I don't want Googles suggestions to be as random as they are. If a user starts typing their street name, chances are that google suggests streets from all over the world but not the one they are looking for. It's possible to feed Google a country and a zip-code, but asking for those two is, again, something user's aren't used to. Asking for those details via some sort of wizard comes to mind, but even that's not something I'm used to seeing for address forms.

So, it all comes down to making the thing as usable as possible. I'm looking for completely different approaches as well, if anyone of you has a better idea or knows a shop that does it in another way.

Thanks for your ideas!