Replace HDD in Sony HAP Z1ES with an SSD

I decided to get the Modwright upgrade to my HAP Z1ES, and I had them install the SSD. So, I can't help you. Sorry. I can speak in general terms.
The HDD native to the HAP will look nearly identical to the one you bought.  
HDDs are usually mounted in fitted racks with (I think) four screws on each rail (that is, each side). The screws go through the rail into threaded holes in the HDD case. The drive will have a ganged connector for power and another for the data bus. Unplug these first. Do this only with the HAP powered off AND unplugged. Remove the screws in the rail and the HDD will slide out easily. Note how it was oriented in the anchor rack and orient the SSD the same. Plug in the connectors, being sure they're properly seated, and slide the SSD in the rack until the mounting holes align. You want the screws tight, as vibration will degrade the performance of the drive. 
Again, that's how it works inside a computer; I'm assuming the HAP is the same, but I've never seen the innards of the HAP myself. 
If you live near an audiophile retailer, you may be able to get advice from someone there. Remember, these things are assembled by people working cheap. If they can do it, you can too. 
Sorry I can't be more helpful. 

OTT,  that was so kind of you to try to help out. I've built many computers and installed lots of hardware inside boxes, so I guess I'll just have to power through and figure it out.  First tries aren't always successful.  It's a LOT of screws to even get the cover off, let alone remove the hard drive from where it's pretty tightly installed.  I'll let you know what happens and maybe take some pictures along the way to help others contemplating the job.  Apparently, there was once a detailed how-to on HiFi-Insider, but that's no longer available (unless someone can help with reposting that article with its detailed photos. MUCH OBLIGED if you can!).

Bakemann, if you go forward with the drive replacement, let me know how it goes,,,pics would be nice.  There is mention of it on Steve Hoffmann’s website blog but I can’t find the website with the pics that was referenced:

https://forums.stevehoffman.tv/threads/sony-hap-z1es-hard-drive-upgrade-tutorial.499612/

Sorry, just noticed that you posted the same link...lol.

The HAP-Z1ES factory service manual can be downloaded from https://elektrotanya.com/sony_hap-z1es.pdf/download.html.  HDD removal procedure is detailed on page 15.