I definitely don't want to be the guy getting the 3AM call, but I don't see how going with a VPS saves me from that. Our approach is to have a semi-hot backup with semi-automated fail-over (hopefully fully automated in the future).

Using a VPS simply gives you the ability to get a new server up and running quickly. You'll still get the 3AM call unless you have automated fail-over.

Usually a good outsourced provider will have measures in place to monitor and pro-actively deal with hardware failures as well as maintain standbys and replacement parts onsite. My point is simply that by outsourcing you don't have to deal with those issues. You might still get the call, but your provider should already be working on a fix.