The save as text only is for documents using Legacy Form Fields. Legacy FFs will work with the older doc format files (Word 2003 or earlier) too. However AFAIK, you won't find a Rich Text legacy form field so I don't believe that is an available option.
If you are using docx files with Content Controls for your data entry - you would use linked CCs and would be able to extract the custom XML Part that contains the 'field' contents. Whilst you would then have the option of using a Rich Text CC, that would be a big mistake because the content in the xml file would be enormous and essentially unusable in any form other than another linked Rich Text CC.
Without seeing your export & version requirements it is hard to give you a definitive solution but if you are going to use docx files in 2007+ versions of Word, I would be using CCs. You can get a useful tool to help CC mapping activities here
https://gregmaxey.com/word_tip_pages...rol_tools.html