Drupal & Wordpress User Integration
This is a rough sketch based on some other projects I've been involved in but the WP part is a bit uncertain. FWIW here it is:

1) install services, rest server and an auth module (like oauth or api_key) the on drupal and create an endpoint with resources for the user functions you need. Find a great tutorial by here. Essentially you should be able to push a php call with the json to your endpoint (Chrome's postman is a great tool to test this with) and get a 200 response if user was logged in or 401 unauthorized if not.  

2) pause WP from processing user tasks on its side 

3) export legacy WP users to csv and import users into Drupal using the user import module 

4) Now you should be able to set ping your drupal from WP, get a reply back, set a session var if logged in and serve content on WP as if they logged in. 

Granted, this is not an ideal setup but hopefully will carry you through the few months until you convert WP to Drupal.