I am from Hungary and I had some success converting books that came out OK. I gave up on Calibre a long time ago (the same formatting mess, that you also mention), so this is for BookDesigner.
First you should install Unicode font support for the Reader from here:
https://www.mobileread.com/forums/showthread.php?t=27177
You must also replace the fonts with the new ones on your PC where the Sony Connect software is installed.
tt0003m_.ttf, etc.
Then use BookDesigner to convert. BD actually supports Czech as an input language (lucky for you).
With this method some of my Hungarian ebooks convert just fine. Still some come out as crap (due to different encoding is my guess).
An alternative is to replace all special characters with normal ASCII characters (should be still readable if you are not too picky).