Priiloader's one isn't system wide, it's only the Wii menus (or maybe that's what you meant?)
vWii is kind of a lost cause imo, it has colour issues that don't seem to be getting fixed any time soon. It would have been so nice to have a Wii U as an "all in one" machine covering 3 generations of Nintendo consoles with clean HDMI output, but that dream is gone for me. I've accepted this now.
I would recommend using an original Wii console with the Mayflash HDMI converter - its AV output quality is solid, and I tried a few others. Your display will have to upscale the 480p to 1080/4k, so the resulting image quality will be somewhat dependent on the video processor in your display. Or you could pair it with a mCable classic to have the mCable upscale to 1080p with its antialiasing and sharpening filters. I'm super curious to try one of these out myself. Actually I want one simply because
according to this poster, mCable correctly converts 480p Rec.601 colours to Rec.709 colours for its 1080p output, which allows me to sidestep an issue where my TV's video processor incorrectly decodes 480p with Rec.709 coefficients, causing eg. Mario's hat to look duller and orange tinted. This always discouraged me from playing Wii, so if mCable can make a nice output with correct colours and good upscaling, this could be my preferred way to play Wii games (currently using Dolphin).