On a freshly-rebooted server why would the CPU running time of processes be huge?

Time+ represents CPU time, or more specifically, "Cumulative CPU time which the process and children of the process have used".

Total CPU time the task has used since it started. When 'Cumulative mode' is On, each process is listed with the cpu time that it and its dead children has used. You toggle 'Cumulative mode' with 'S', which is a command-line option and an interactive command. See the 'S' interactive command for additional information regarding this mode.

Source

Here's a link explaining CPU time if you're curious.

As suggested by @jski, a full cold reboot of the machine has worked.

The Time+ values of top have returned to (pratically) zero.