Using a drop down list for Authenticator OR populate drop down directly from contact list

We have a survey in which the respondents first identify their organization, then that data is used to pull in related data for other parts of the survey (as well as let us know which organization is responding).
This would be straightforward if each org had a password or unique id they could enter. We'd set up an Authenticator and contact list. But in this case we want each org to be able to select their org name and move on. Is there a way to make the text field for an authenticator a drop down or autocomplete?

An alternative solution would be to use a regular dropdown and call the rest of the data via the API. In this case the challenge is that our list is almost 1000 long, and ideally we'd collect the org id while the user selects the org name. Is there a way to populate the drop down based on a contact list?

(Planning on using JQuery to turn the drop down into an Autocomplete in either situation.)

TIA!