I've fixed the issue within what I think is satisfactory. I'm going to assume that it's a permission issue between SQL Express 2005 and Server 2012 R2. For whatever reason when it initiates the BACKUP DATABASE command it can create the BACKUP folder, the corresponding folder with practice-date-timestamp, and then the AmazingCharts.bak file. The file size never reaches above 0. I'm guessing its related to a security thing with the Program Files (X86) folder and a MODIFY permission.
To bypass this and basically make it think it was still using the BACKUP folder I made a symbolic link to a folder on the data drive. Ran the backup utility, and finally ended up with a fancy little backup zip.
From the CLI and in the Amazing Charts folder:
MKLINK /D BACKUP "E:\Backups\Amazing Charts"
Bert,
To appease your fascination, he basically generates some report with the patients information with his hosted EMR and then copy/pastes that data in one chunk to Amazing Charts. This is merely for his peace of mind in case he loses internet or something for an extended period of time. We're well within tornado alley so it's not too far fetched to think connectivity could be down for an extended time.
Everything seems copacetic on my end now. Thanks everyone for the help. Hopefully this can help someone else in the future

Tristan