@bigwave1 I'd go for upgrade of operating system to start with. Mac OS upgrades not that difficult, go to an Apple forum to learn how. Now, the one issue is since your present OS optimized in some form, may not seamlessly or even be able to do OS upgrade, in which case you bricked your MM. At this point you'd need to install new ssd with latest Mac OS installed, also doable. I could directly guide you on this via private email, can't provide any direct service to you as breaks Audiogon rules as far as selling services or products. So, best and safest path for you, assuming you brick present ssd doing OS upgrade is install of fresh OS on another ssd. This requires physically removing old ssd and installation of new ssd (ssd is your hard drive). PCIe is simply another form of ssd, not sure 2013 MM capable of using, not something to worry about at this point in any case.
So, personally, I'd keep MM and perform the OS upgrade, assuming you can diy or find someone who provides service. Ask at audiophilestyle forum as that is goto forum for streaming, dedicated to computer audio. You could also speak to Mojo Audio or Alex at Uptone audio, both have experience with MM upgrades, may be able to help you or put you in touch with someone who could.
If this all seems too daunting, you could get another server, NUC would be lateral move IMO, so would most others at sub $5k. I'd consider Sonictransporter I9 an upgrade, very nice processor and optical out built in, also has built in hard drives for storage if present Synology is too much hassle. You can simply transfer your present HD's in synology to I9. Get OpticalRendu as streamer and you have first class setup, Keep in mind this designed to be used with Roon. You could run Audirvana, but would require some diy work. This all runs $5k.
So, if prepared to spend some money, get I9 or some other server, or save yourself the money, keep MM and prepare for some diy work. While it may be possible to simply pack up MM for hotrodding, not sure I'd count on it. Best bet is the diy attempt at new OS install on present ssd. Other easy route would be to get someone to sell you new ssd with present mac OS already loaded, requires the physical removal and install of ssd, special tools required as well. Go to ifixit.com for videos and pictures that will illustrate whats required.
Wish I could help you directly, I could get that mini up and running in little time.