You could potentially copy/paste the actual cells vs. their content. Here's what I mean:
CopyToClipboard[NotebookRead[Cells[NotebookObject[obj],CellStyle->"Text"]]]
Then Paste
:
Paste[]
The Text
cell style renders properly outside of the notebook front-end, and you'll need to convert all your Input
cells to Text
cells first, but that is pretty easy to do: you can alt+click on an input cell in the notebook and it selects all of the cells of that style. Then, you can do ctrl+7 to turn them all into text cells.
Hope this helps!