You will have to cleanup the Word file provided by the export with MS Word.
Export is very much a function of the "input" (what made the PDF, how did this make the PDF, etc.).
So if the authoring file had poorly mastered content and /or the process used to create the PDF and the "how" of this is off then you have "GIGO".
Garbage In = Garbage Out.
When the PDF file's "under the hood" stuff is good you have "GIGO".
Good stuff In = Good stuff Out.
So, the caliber of export is always going to reflect what is fed to the export process.
What will optimize export is having a well-formed Tagged PDF (a PDF that is ISO 14389-1, PDF/UA-1 compliant).
Two core aspects of "tagged" PDF are (1) Accessible PDF and (2) useful export of PDF page content.
Be well...