Where were your local files downloaded from? I went through this last night, easy fix if you know what to look for. It's not Spotify, your software or storage. I'm thinking if your local files weren't downloaded from a trusted, verified source, you won't be able to import them in to Spotify. I used to just do a mix of ripping audio from YouTube using some third party site, or purchase from iTunes  but I would also download free mix tape tracks that weren't available for purchase, from a specific, verified place like  datpiff.

Well long story short after going through every troubleshooting step I could think of: restarting computer; deleting and reimporting playlists, verifying wifi and even updating iTunes, I realized the only songs that were stuck waiting to download were the ones that came from the third party ripper. So I deleted those and redownloaded them all from the working source, in my case, datpiff.

Voila, music available offline in both my phone and iPad, it even synced to my boyfriends android. I only had 5 songs I wanted to import, (Spotify has almost no Chance the Rapper) so it didn't take too long, might be a hassle if you have much larger amount of music but that's what worked in my case. Try it with 1 or 2 songs first and let me know how it goes.