How to quickly fill holes in iPhone music collection that are in iTunes on Mac

My complete music library is about 6,000 songs on my iMac. Currently, I have about 4,000 on my phone because I used a bunch of space for apps that I no longer need. Is there an easy/quick way to upload the remaining 2,000 songs to my phone if I don't remember exactly which songs are missing? If I try to move my entire library to my phone will it just skip the 4,000 duplicates or will I get everything?

If deleting and reinstalling all of the music on my phone is the way to go, then will that ruin all of the playlists I have on my phone? If so, is there a way to preserve the playlists so I don't have to spend a ton of time recreating them?