Ok, now the updated mock-up makes it clearer :)
The following might be a good argument againts a dropdrown or combobox (what's actually the standart term for this interaction device, never found out g)
Nielson/Pearce write in "Eye Tracking Usability" about the phenomenon of input field dominance that they observed during their studies. I remember this very well because I observed the same behavior in my own eye tracking study for my bachelor. To make it short: There seem to be nothing more dominant than any kind of input field on a page. Even if you write above "don't look at the input field", you'll mostly observe, that people first look at the input field and then at everything around it.
To get the connection to your issue: Providing a dropdown might get the users away from voting online, because they're going to interact with the dropdown instead, that is only there for... well, what actually? Displaying adresses of the five (!) stores? IMHO that's not even the best practice, because your present mock-up allows to scan the adresses much faster and with less interaction then via a drop down. And the adress is presented completely at one glance. The only interaction required is to open up this list; via a mouse hover I guess? In that case I would work a little bit on the wording to make clear that you have to hover (or even more "below threshold" like presenting it as a link and once the user hovers over it, it already shows the list).
Sorry for not quotating the book exactly, I don't have it. I read it when I was working on my study, so I don't know which page the phenomenon is described.
One more argument against dropdown: What items should the dropdown contain? The names of the five stores? So the user will have to choose a store first and see the adress then, just to realise the store isn't anywhere near her, making the interaction a trial and error trip?
Hope this can help when you meet the HiPPO again.