Must I re-make up missed prayers that were prayed out of order, knowing that they were made up incorrectly based on a misunderstanding of the obligation of order, and their number exceeds one hundred?

Scholars differed regarding the obligation of ordering missed prayers (fawait). Whoever failed to order them, their prayer is not invalidated, especially if they were ignorant. Therefore, the questioner does not need to re-pray what she made up of unordered missed prayers. She must maintain regular prayer in its prescribed time and make up future missed prayers in their proper order, out of caution and to resolve the difference of opinion.