How To Obtain All Twitter Followers Without Hitting API Limit

I don't think there is any way round the limitations imposed. Even tweetbot has this limitation, as it's a limitation twitter impose. You could create a note in the database of the current status and set a cron job to run every 15 minutes which would run a group of requests again. It will take time, but it could notify you via email when it's finished. That's what services like socialbro do. You'd cache those results in your database of course.

This a way faster, but there's a limitation concerns also :

1- make a request to get all followers ids ... paging with 5000 id in the page https://developer.twitter.com/en/docs/twitter-api/v1/accounts-and-users/follow-search-get-users/api-reference/get-followers-ids

2- loop on the ids and send each 100 id in a comma separated string to get their info https://developer.twitter.com/en/docs/twitter-api/v1/accounts-and-users/follow-search-get-users/api-reference/get-users-lookup

3- now u can get 1500 user object instead of 300 user object every 15 minutes

But you need also to set a timer every 15 request in case the followers list is more than 1500