@ame54 - As per my knowledge, currently there’s no way to handle many to many relation without duplicating the data at the dataset level. What we typically do, it create calculated fields using various LAC functions to get the correct/intended/de-duplicated results.
Since, Quick Sight doesn’t provide any way to model the data with defined relationships while keeping the tables separate, the bridge table solution will also not going to work at least at this point of time. Hope this helps!