Mac mini mid 2010 stuck on Apple logo with full progress bar
So, I finally found a solution. The verbose boot lead me to believe that the problem had something to do with the FireWire port/driver. Since I do not really need FireWire, I figured I could disable it. Therefore, based on a combination of other answers to similar questions, I did the following:

First, I must disable SIP, so I can use the Single User mode with writing privileges. Since I cannot boot into Recovery mode, I used Single User Recovery mode, by holding Command+R+S (as suggested in https://superuser.com/a/1245838). From here, I just ran csrutil disable command to disable the SIP. Reboot.

Now, I need to deny the kernel access to the IOFireWireFamily kext, in order to disable the FireWire support. Allegedly, this could be achieved using several methods, such as chmod 000 the kext, moving it, unloading it or deleting it. I went with the last option. For this, I followed these steps:

Enter in Single User mode (Command+S)
Give writing privileges to the user by running mount -rw / (https://www.insanelymac.com/forum/topic/285013-how-to-use-single-user-mode-and-how-to-use-it-to-uninstall-kexts/)
Deleting the kext file using rm -rf /System/Library/Extensions/IOFireWireFamily.kext (https://discussions.apple.com/thread/1805732)
Reboot



Now, the system does not look for the faulty FireWire port/driver anymore and it boots into High Sierra without problems.