I do this a lot in Asia and never even have to check out, so it must vary a little by hotel and region.
Sometimes my room key stops working properly but I've found room keys so iffy that I barely notice.
I like the idea of emailing the hotel and seeing if they will do the one flat rate. Another option is for them to give you the whole two weeks at the average price. It won't save you and $ but means only the single booking number and makes it easier (I assume) for them to upgrade you, etc.