Acrobat does have an accessibility check that you can use, but I don't know if it will suit your needs. My guess is that converting to HTML would not be reliable enough.
In Indesign, reorder ALL the objects on page using send to back, starting with the last object on page you wish read, continuing until the object you want read first in acrobat is sent to the back last in InDesign. The result is that the Reading order is correct in Acrobat. Obviously, any object additions to a page means re-ordering the whole page. Changing copy doesn't affect this. Also, the order of objects on a page has no relationship to the page structure. It appears that the object reading order is as objects are added to page. Ist added (and furthest back), 1st read, last added (nearest front), last read. Shuffling the objects in the Document Structure pane has no effect on this order (and vice-versa).