I've recently been trying to get Catalina patcher to work for a macmini4,1 and imac10,1 (very similar hardware) but I've been having no luck at all.
Both systems are currently running fully up-to-date High Sierra installs with boot ROM support for APFS, though neither system is currently using APFS on their internal drives (as they are stock HDDs I'm going to replace), however I'm not installing to these.
I'm installing clean to an APFS formatted SSD in an external USB enclosure, my intention being to get the systems ready in advance of swapping in the SSDs, while leaving the known good High Sierra installs untouched (as it turns out, a very good precaution to take 😉).
I was able to get both systems working with Mojave installed in this way using dosdue1's Mojave patcher, but I have thus far had no luck with either system using dosdude1's Catalina patcher in otherwise identical circumstances.
To install Catalina I'm using a USB installer created with Catalina patcher from a copy of Catalina downloaded by the patcher as well. Installation proceeds as expected, however when I progress to the point of starting up from the finished install (not the installer volume), all I get is either the grey Apple logo and no progress bar, or if I get a progress bar it advances very slowly, in both cases no matter how long I leave it the system it never finishes starting up.
I also haven't had any luck in finding any clues as to what might be wrong; I've tried starting up in safe or verbose modes but neither seems to work (exact same boot screen, no extra information). I've also tried booting back into the USB patcher to run the post-install patches (with force kext cache rebuild) in case patching was being skipped by the installer, but that doesn't work either. I've attempted to do the install now three times, with a fully erased disk two of those times, it has made no difference.
Everything seems to suggest I should be able to install Catalina on these systems using the patcher, but it just won't work. Is there some incompatibility between the current version of Catalina 10.15.7 and the latest patcher (1.4.7)? Maybe a security update that was integrated and breaks one of the patches or something? Is there anything else I can try?