I've just watched both of these with VLC and processed them with MakeMKV to turn them into MKV files. They look the same in both cases; though the timing is a bit different with the IFO files.
The "escape" files made MakeMKV give a big warning that they had been processed with DVDFab and were "broken". I'm assuming this is because you reduced the quality of these so they could be uploaded?
You're probably wondering why I didn't try the raw IFO/VOB files in MC. It's because I use MC for Mac, which does not have DVD decoding capabilities. MC for Mac can read any kind normal video file, but not DVD or BD structures.
After turning both of these info MKVs, MC reads them fine and displays the subtitles as I expect them. There are only 3 total lines (subtitles) in the first video, but they seem to be on screen for the right amount of time and there is no overlap. In the second file, I see many, many lines of subtitles, but again, no overlap, and the line at ~2:33 is definitely there.
Since you have thousands of DVD structured files, I know it's impractical to suggest that you convert them all to MKV. What about converting a few of them? Like these two titles. That would seem to be a reasonable test. How many problem files do you have?
Brian.