I'm not sure if it will improve anything, but it will be done properly. I guessed correct and did right the first time, but the stock files for the Intel program weren't correct, so some things may not be set 100% correctly in the ME FW.
I can remove any whitelist I can find, but I need to know the error given (otherwise that's not a whitelist block) If you are not getting any error like "remove device to continue boot" etc, then it's not due to a whitelist or block/allow list, it's probably due to some setting needing to be set to something else instead. I will check out all related settings I can see for that and show them to you, maybe you'll recognize something that needs changed. I'll gather than info up and redo the ME FW and get back to you soon.
*Edit - Forgot to mention, wow hot swap PCI/PCIE while up and running, sounds like a scary thing to do, I can smell the ozone possibilities
* Edit - I checked BIOS for this PCIE port issue and here's my thoughts and findings
Possible causes from what I see as being related (but may not all be)
Boot option filter >> Set to Legacy only (Could be set to Legacy/UEFI Both)
Under ^^ Option rom settings >> Video = Legacy First (Could be set to UEFI First, if eGPU uses UEFI vBIOS/GOP)
^^ ^^ >> Other PCI devices = Legacy only (UEFI Only is only other option here) could need to be UEFI is eGPU uses UEFI vBIOS/GOP
Similar to above, at Boot Menu >> VGA Support - currently set to EFI (can be auto = legacy, if egpu has only legacy vBIOS this may help)
AT Debug folder (no name, under MAIN in AMIBCP) GOP Driver - at optimal defaults = enabled (thus unloads vBIOS and uses UEFI GOP, opposite for disabled) Speaking of this folder, look at all the settings there for PCIE 3 (any look like they would help being changed?) Mainly these are error reporting, other than ones I mention below, but there is ASPM (Active state power management) which isn't in the normal PCIE area settings.
PCI Express Port 3
Speed >> Set to 2 or 1, instead of auto - basically test both, see if either helps or changes what happens
Extra Bus Reserved << Maybe it needs something set there?
Reseved (SP) Memory << Same as above
Prefetchable Memory << ^^
Reserved I/O >> Currently set to 4K, many options
Other than all this, if you are not getting any error then it has to be something in the above settings, otherwise if there was a whitelist or blocked list etc you'd get an error telling you to remove device etc or a non-boot situation with/without error.