ticket at Fortinet support first said 6.0.5 --> 6.0.8 would be possible, but then came back that 6.0.5 --> 6.0.7 --> 6.0.8 would be better / more safe, so it will be an extra step for me.
FortiManager / FortiAnalyzer 6.0.7 will work fine with 6.0.8.
port seems limited to 8888 and 53
fg-grtpr (fortiguard) # set port
8888 port 8888 for server communication.
53 port 53 for server communication.
as for that piece of configuration (set protocol https) it makes me wonder about 6.2.x, if you have protocol set there to something else then https (checked some and they are set to UDP), is it safe or not?
if your FortiGate is behind another firewall then you might have to change things on that other firewall allowing tcp/8888 probably.