Based on the responses so far, it looks like the answer is: No, there isn’t currently a speech recognition software that works really well on LibreOffice.
It sounds like some people (e.g. @jpnelson40) have had okay experiences with Dragon, but that they, too, have experienced some pretty significant inconveniences.
You mention that Windows speech recognition works (separately) for you, so perhaps there are two things we should do going forward:
@SoWhy - Please file an enhancement bug and ask for better support for Windows speech recognition for LibreOffice on Windows. Don’t forget to mark your bug as an ‘enhancement’.
@jpnelson40 - Please file a bug about any interaction issues LibreOffice is having with Dragon. If the bug is an issue upstream, then we can send the bug to Dragon. If the QA team thinks the bugs are more of an ‘enhancement’ than a plain bug, then they can recategorize your bug as such.
Please post a link to any bugs you file in a comment below using the format “fdo#123456”.