After Mojave install I get a "No WiFi hardware installed" when trying to connect the wife. Computer response is so slow it's almost useless. Same results on iMac 27" Retina Display Mid 2015 and Mac mini Late 2012. Tried NVRAM and SMC resets to no avail. iMac worked fine when I reverted back to High Sierra but backup for mini is on the WiFi network.
I edited the /etc/sysctl.conf file. There are three settings adjusting socket buffers to improve broadband performance. I doubled the numbers there and it fixed the networking issues. There was a constant stream of error messages saying sockets were unable to allocate buffer memory. Apparently, there is a process crashing somewhere and not releasing it’s socket buffers. I don’t know which one is doing it because it is hard to track down due to the sluggishness.
Just so you know, you're not the only one with this issue.
I can't help you with fixing this issue, but I can offer advice on restoring the backup on the WiFi iMac:
I was able to manually reconfigure the wifi when booted in to recovery mode by clicking on the wifi icon on the top left. Wifi showed 'no hardware detected' when booted in Mojave, but it DID work when booted to recovery mode - So you should be able to restore the mac mini that way.
( FYI, I have the exact same problem you're seeing, also with computers I just upgraded - An iMac and a MacBook pro. This may imply that it has something to do with software or extensions we've both installed. Unlikely to be kernel extension, as safe mode is supposed to disable 3rd party extensions. Like you, I also tried Resetting NVRAM, SMC etc with no luck.
Did you have the issue where the bluetooth keyboard and mouse were no longer detected in Mojave as well on the iMac? I needed to plug in a USB keyboard.)