Read PS4 hdd with PC

Ok, I bought a new PS4 Pro and low and behold our Plus membership ran out a long time ago and for some reason I had no idea so none of our game data was saved to the cloud. I can’t keep the old PS4 running long enough to do the lan cable data transfer so now my only hope of restoring game saves is to somehow get them off the old console’s hard drive, on to a usb and into the new console. I’m sure there has to be a way to do this as I’m 100% sure I’m not the only one who has had a console shoot craps before game save data was saved. I just can’t figure it out right now. Back in the PS3 days I could easily do this but then again I still ran XP and I had all sorts of boot time tools that I could manipulate hard drives with.
I still run 7 but have no boot time tools. My issue at the moment is I have the hdd hooked up externally using a SATA/usb3 interface. I can see the disc in disc management but it will not map and assign a drive letter. I cannot see the volume in My Computer like I can with my two hard installed hdd’s so I can’t manipulate any data on the drive.
I’ve even emailed Playstation support but have not heard back yet.
Has anyone successfully pulled saved game data from a broken console’s hdd and got into the new system and how did you do it?