Hey David, I actually just upgraded from Tableau Server 6.1.5 to 7.0.0 without any issues. I was able to browse the workbooks that were developed in Tableau Desktop 6.1.5 on Tableau Server 7.0 after restoring the backup. It's odd to hear your issue though, because what I've read in the Desktop and Server Compatiblity article that Tableau Server is backwards compatible with 6 & 7.
Hope that puts you a little at ease.
I will add that I noticed a performance difference with Tableau Server 7.0 running a report developmed in Tableau Desktop 6.1 versus TD 7.0. TD 7.0 report performed much better than 6.1.