You're right Tony. I just found out about this setting in Handbrake. If I uncheck it I can put multiple subtitles into one MP4 file as well, so that's bonus.

The subtitle location is still bad, but indeed, in VLC I can pretty easily move the subtitles lower. Which is what I will do.

Thanks for all the help guys! Seriously!

Now I'm in doubt if I will compress the ISO's using H.264 or H.265. H.265 compresses about 30 to 40% better than H.264 does, but it takes up to one hour for a 90 minute movie to compress, while H.264 takes a mere 8 minutes. Oh well, guess I'll only be doing this once, so I might as well do it right. It'll take me months though...