I confirm your test results. With SIP always fully disabled, installation of 10.15.4 with patcher 1.3.1 never failed even when removing all AMFI tranquilizers before.
(Always using a bootable USB installer, didn‘t try install-to-this-machine as I don‘t have patcher 1.3.1 anywhere else)
MBP5,2, APFS ROM patch applied.
Did more testing, and finally I'm happy that I got some non-working setup.
1 - removed /Library/Preferences/com.apple.security.libraryvalidation.plist
2 - made sure that /Volumes/Preboot/xxx/Library/Preferences/SystemConfiguration/com.apple.Boot.plist and /Volumes/Catalina Data/Library/Preferences/SystemConfiguration/com.apple.Boot.plist contain as kernel flags only -no_compat_check
3 - made sure that nvram boot-args contain only -no_compat_check
All that I already did in the previous testing. Then in order to get rid of any other hidden state I reset nvram and SMC.
I did not re-disable SIP at that point (resetting nvram does enable SIP if I'm not mistaken).
Then used the existing bootable USB installer with 10.15.4/1.3.1 to install over my existing+working external 10.15.4 SSD.
Also did a clean install on a freshly erased APFS HDD.
In both cases:
-> installation went fine through the three phases (Catalina logo, short grey-on white phase, long white-on-black with remaining-time display).
But the resulting system won't boot. Inspected that SIP is disabled at that point and that .libraryvalidation.plist is in place.
Added amfi_get_out_of_my_way=1 to boot-args in nvram - still won't boot.
When watching the boot process in single-user mode, the usual AMFI complaints are shown, leading to an endless grey-on-white booting phase.
Repeated the installation. nvram has csr-active-config w%00%00%00.
-> same as before! installs fine, doesn't boot.
Now I'll do csrutil disable from within the terminal of the bootable USB installer and install again... I'll report the result.
So far I guess that confirms the SIP hypothesis, unless I have reset some other, hidden state as well.