Until your specific issues/requests perhaps get addressed, I have some advice.
I also have some very hi-res images of albumart. (often photographs of LP covers)
I store them unprocessed in the album (sub) folder as a source, but they are not very practical or useful in a mediaplayer, MusicBee included.
So I process them with Photoshop, square them, fix them up a bit, and save them as jpg at maximum 1600x1600.
The filesize is always less then 1 MB, they look absolutely perfect in MusicBee, and I encounter no issues with them at all.
Also I hope you realize that for example a 1500x1500 good quality jpg will beat a 1000x1000 png in picture quality every single time, and will probably be something like a third or less in file size.
I'm sorry that this is not an answer or a solution to your questions, but I hope it's something useful for you to consider.