While rate limits for those are restrictive, friends/ids and followers/ids can get 5000 ids per call - are you hitting limits even with that? Getting rate limit increases / whitelisting doesn’t happen often - maybe you could get away with requesting fewer ids per user (max 5000 in 1 call). Since each endpoint has it’s own rate limit, and rate limits are per access token, each one of your app’s authenticated users should be able to make 15 calls in 15 minutes to both /friends/ids and followers/ids.
Also, you could fall back on friends/list and followers/list (retrieving 200 full user objects per call, not just ids)
Most likely thing you’ll need to fill out is “Special Permissions” Platform Support Form: https://support.twitter.com/forms/platform