2012 Mac Mini with HDMI issues (multiple)

I have a late 2012 (November) Mac Mini 2.5 Ghz Intel Core i5 that is having HDMI issues. The Mini is hooked up through a Sony DA5200ES receiver to a Sony KDL46hx750 TV HDMI > HDMI and I am using a quite expensive (100 USD) directional (yep it is correctly installed) HDMI cable. The main use of the Mini is to serve as a media player (Plex) and I have made sure that all the settings in the receiver and in Plex are correct. The Mini is always on and I have checked to make sure all options to have it always on are selected.

I have searched both the Apple support site and the Plex site and found other users with similar issues but not found a resolution. Here goes.

Here are the issues.

The Mini reverts to 720p almost each time I either turn the TV on or switches HDMI source to the Mini on the receiver. With almost means that it can happen every time or a couple of times. Sometimes everything is fine though. This is frustrating, especially if I have forgotten to exit Plex as there is no way to come back to the desktop to change screen resolution other than to do a hard reboot of the Mini. When I first installed the Mini it opted 'best for display' option which is 1080p. When I start or restart the Mini it always picks 1080p as default. I have tried switching to an Apple HDMI cable but to no avail. The first couple of days it was noticeable better but not anymore.

The resolution ⚠ I have tried is to update to EFI 1.7 but then my Mini tells me that the machine is not allowing the update so I guess I already have that firmware. Some people on this community have seemingly solved their issues with this firmware update. If I do not have this firmware update I might have issues #2 here.

The other issue I have is that I sometimes get picture black outs (very short, like a second or so) when either I select the Mini through the receiver or when I start Plex or when I start a movie or tv-show in Plex. I guess this is a handshake issue but this I did not have for the first couple of weeks. In fact I believe this issue came with the latest software update OR when I changed to the Apple HDMI cable. I did not have this issue with the original HDMI cable I used but now when having switched back it is still there.

The latest (hopefully the last) issue I experienced this morning when firing up the TV. The display was as usual scaled back to 720p but when I switched to 1080p the desktop did not resize so I had the nice milkyway desktop in the top left corner of my display but the rest was white. All icons where there still though. I had to restart the Mini to fix this as selecting desktop options (new images, etc) did not help.

Any friendly soul out there that has any ideas what this can be about and how to solve? While this is not a show stopper for me it is very frustrating. Especially as I have been a Windows PC guy for the past 15 years but have during the past year 'collected' an iPhone, a couple of iPads, a Macbook Air and an Airport Extreme.