If handbrake is messing up the fonts, I'm assuming the soft subs are in .ssa/.ass formatting. An option would be to extract these files with MKVextract, use Aegisub to convert the fonts in the file to an installed font on your computer, then use MKVtoolsnix to remux the new subtitles into the original file. It sounds a little tedious, but it only takes a few minutes for each file.