You already know the answer and are trying to avoid it. Odin is the most reliable way to apply an update. OTA updates fail for numerous reasons and we couldn't begin to guess why in your case because you provided almost zero information about your phone e.g.what was the exact, verbatim error or failure message you received, have you frozen any apps, syslog, current firmware version or anything else.
We don't have your phone in front of us, so when you don't describe those crucial details, the best we could possibly do is make stabs in the dark as to what is going on.
If you do a proper backup, restoring your programs afterward shouldn't be that hard. You could probably just restore your backed up /data partition over the updated system and have most of your apps and settings restored in one swoop. Alternately, you might be able to apply the new firmware image with mobile odin pro, while leaving your existing /data partition intact.
Or disable the OTA update manager to avoid the update. Verizon likes to rename or at least append vzw to system apps, so search the Verizon forum for the name of the Verizon OTA update manager app.