Adding "Composer" changes file duration

You could have left the cover as it is.
Simply loading the files into MP3tag and then press Ctrl-S to save the tag again (without APE) but this time in the set tag format (in your case: ID3V2.4) removes the flawed ID3V2.2 tag and overwrites it with a properly format tag.
So, in fact, MP3tag is a helper to remove the problems and not the cause.

When you resized the picture, the tag also got rewritten as you can see: now MP3Diags says that you have an ID3V2.4 tag instead of the uknown, malformed ID3V2.2

For MP3 files only the settings in the top screenshot are relevant - and they are OK IMHO.
(Personally, I would still use ID3V2.3 as that is more widely spread.)

The settings in the bottom one are meant for other file formats:

I don't think that is correct, nor in line with your comment above about cover image size being a factor. When I did Ctrl-S, even after unchecking the "write APEv2" box, that broke the files. Only after I reduced size of embedded cover art did the files save correctly.

Here is a screenshot of what I have done so far:
downloaded the 3 files.
made a copy of "Aria" and saved the tag.
Then tried the same to find out whether that was just a freak observation or not.
Now, as a consequence of your doubts, I took the 2 remaining files and created a copy of each (they have _kopie at the end of the filename)
Loaded them into MP3tag
Pressed Ctrl-S for the copied ones
Started MP3diags for analysis.
This is the result:


The 2 "kopie" ones are now OK and show only minor quirks like missing normalization.
The original files show many more peculiarities - all the broken threads and stuff as we already know.
But as you found a method to get your files fixed, everything should be ok now, I would think.