For now, I've settled on using HTML5 datalists in conjunction with a modified <paper-input>
control (I've submitted a pull request to the Github repo to merge those changes back into the master branch). All those changes do is persist the list
attribute to the inner <iron-input>
control so that it can utilize an HTML5 datalist.
Definitely not ideal, but, in the short-term, it'll function as a placeholder in place of a real typeahead control.
I also built a quick custom validator that iterates over the same Array collection as what I use in my datalist so that the <paper-input>
control knows if the current value is a selectable (valid) value or not.
Edit: The best place I've seen to bring up a first-party developed autocomplete is on the PolymerElements/paper-elements repo on GitHub. I'd discuss at https://github.com/PolymerElements/paper-elements/issues/26.