🚀 go-pugleaf

Not a bad idea... particularly if you build the spellchecker in such a way that you can run it before you even flow the text into InDesign (thus avoiding not only spelling errors but layout adjustments arising from corrections).

Wherever you check the text (OS or TextEdit), you could apply the changes to formatted text in InDesign if you use the find and replace method, omitting any formatting preferences. Keep the original and corrected text separate, log (or find) any differences in the text and swap them out. You might need to search for word triplets (a word before and after the correction) to avoid global changes (but if you do this you'll want to ensure that the triplet doesn't cross a paragraph break).

Or you could correct the text a paragraph at a time (presuming you're not using character stylesheets) - that way you can just have your script remember the stylesheet (or paragraph formatting properties) and re-apply them to the corrected paragraph.