I have been running High Sierra on my 3,1 2008 8-core Mac Pro since September 2018, using DosDude1's installation. Has been relatively problem-free, though sometimes feels slower than El Capitan. One fault that took me a while to fix was random logouts for no apparent reason, but I pinned it down to a conflict between my GPU's. I have an unflashed EVGA Nvidia GTX 760 which performs well, and gives me CUDA in Photoshop and After Effects, but when problems do arise it's handy to be able to see the EFI boot screen, which I can't do with the PC Nvidia card, so I left the old ATI Radeon 2600XT installed powering a small monitor. This never caused any problems in El Capitan, but seems to be the cause of the random logouts, as they haven't occurred since I removed it. I installed a later Atheros Wifi card shortly after buying the machine, as the machine came without Wifi, and there have been no problems with High Sierra and WiFi.
DosDudes Patch Updater allows AppStore system updates to run. I ran a security update in November without a hitch, but since running the last update earlier this month the system has been prone to very slow system boots and boot freezes, so I have made a USB installer using the latest download and patches and intend to re-install the system.