Sync old iMessages from iPad to new iPhone
So I haven't backed up my iPhone in a while, and it had to be replaced without the opportunity to back it up (water damage, dead dead dead). I can restore the new iPhone from the last sync I had, but that was months ago. Everything else isn't really important, but I'd like to get all my iMessages from the time between the last sync and now onto the new phone if possible. The thing is, all of those messages are on my iPad, which IS currently backed up. I don't, however, want to restore my entire phone contents to the backed up iPad, JUST the iMessages (the iPad has a ton of stuff I don't want/need on my phone, and the phone doesn't have enough room to hold all the iPad contents anyway). Is this possible? Does anyone know how this might be accomplished? Thanks!
iPhone 6, iOS 8.4, iPad 4th gen