Are you able to share the task list so that each project member is able to fill out their best and worst case estimates on their own in an async fashion, preferably anonymously?
Vistimo Quotes is specifically for producing rapid estimates that don't require team buy-in, sign-up, etc.
Vistimo (https://www.vistimo.com) does anonymous, asynchronous team estimation -- but the additional labor costs (sufficiently describing tasks to async folk understand them, managing team permissions, requesting reestimate when requirements change) have made it not particularly viable as a product.
Finding a balance of power and simplicity is never easy.
It's possible that people may give better estimations when thinking about the number of tickets because then you immediately have to think about the number of individual components whereas with time, you're going more by feeling.