Q: iTunes backup won't work ... iCloud won't either

I was planning on buying a new iPhone yesterday, so I hooked up my iPhone 6 to my MacBook Retina. I backed it up to iTunes, and when it was about 95% done, it just froze. Finally, it said "backup could not be completed because there is not enough space on the MacBook" ... well, my MacBook has 300 GB free, and my phone has space too. I tried several more times, and these had the same issue -- 95% finished, then the backup would just sit there and not finish. Sometimes the backup would end up on my computer, but I would have ~8 GB of data from my iPhone that didn't appear on the backup. I tried again just now, and it said the backup was corrupt ... I've tried everything -- changing ports, restarting both devices -- I even bought 200 GB of iCloud storage and tried to backup my phone last night. Well, when I woke up, it was still showed "estimating time remaining," so I had to give up. Now, I've wasted the iCloud upgrade, can't seem to complete an iTunes backup, and can't get a new phone until I figure out how to solve this issue. I even brought it to the Apple Store and the technical manager or whoever was in charge of these kinds of issues couldn't help me. I'm now in a different city that's an hour and a half from the nearest Apple Store and I have found zero solutions online. Help!