EDIT:
@andjules - I'm leaving the post below, since it may still help, but my first thought after re-reading your post is that you must have 3 EFIs and the BIOS is disabling 1 of them. Is that the case? I'm guessing, but I have an HP Envy x360 15m laptop that I hacked (it is a perfect hack after much work). The BIOS on the laptop permits a single EFI, so I have the OC 0.7.0 EFI on my m.2 NVMe SSD and no EFI on the SATA HD (used for backup and time machine). Again, I'm guessing, but you may have discovered a "2 EFI limitation" with the HP EliteDesk BIOS. I'll leave my post below in case this guess is wrong.
Note: on my 800 G5 Mini, I configured the BIOS boot options so that the M.2 NVMe drives are bootable and the SATA HD is disabled (not a boot option). I have never tried/tested 3 bootable drives in the 800 Gx Minis.
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@andjules I have no issues with 3 drives (2 M.2 NVMe SSD, 1 SATA HD). I use 2 WD Black SSDs and a Toshiba 2TB HD.
Are you certain that your BIOS settings are exactly as I described in the PDF attached
here? What brand of NVMe SSDs are you using?
Please post your sanitized EFI.
One thought - my power supply is 95W. Could it be that your 35W rig has a 65W power supply? Maybe this doesn't source enough current for 3 drives? Also, the 35W rig does not include a 2.5" drive caddy fan. Did you install a drive caddy fan? If not, I would recommend that you install the drive caddy fan, because your 3 drives are generating some heat.