Not a chance I would be performing backups at the clients location. Takes too long and I have other things to do. How long is a backup taking you to make on average? Then how long are you spending on-site taking care of the actual issue? Just some quick, likely faulty, math here:
3 hours drive time
~1 hour for full backup?
~2 hours for repairs?
If so, 5-6 hours per client? Practically the whole day for one client.. don't see how that could be profitable unless they're paying out the ying-yang for travel expense and hours billed. Not saying your business model is flawed, but it sure wouldn't work for me.
If I were to perform on-site backups.. in the interest of speed I would probably carry around a bare 2TB hard drive and go the SATA route direct to the MOBO, the next option would be going with a 2TB USB 3.0 Dual drive RAID 1 of some sort.