Agreed, per the T&Cs they are likely to reprice and charge you at the "Best Available Rate", so some kind of standard rack rate, that is likely (but not certain) to be the more than the equivalent room rate for another night (i.e. 6 normal nights would be more than 7 nights on a long term rate), so I'd agree the best plan to save money is to just keep the room for the extra night - but the OP is correct that this will mess with their plans to gain points from the W (which would be blocked, or vice versa, this 7 night stay would not credit if the W came in first). The typical response when you ask Marriott in these scenarios is they ask which folio you want, so you'd get to choose between 7 nights and 7 nights points at the cheap hotel, or 1 night plus 1 nights points from the W. I don't think they will let you pick and choose from multiple folios, but I could be wrong

As such the choices would be:
1. Just suck it up and stick with the original hotel, and perhaps go to the W a day later / not at all
2. Check out and accept the repricing, moving to the W for another night
3. Put the points from the W to another Marriott account (E.g. a partners or friends) and then you still earn the double points, but probably not any status bonus (if a partners you can then always combine the points when making a redemption)
4. Double dip and stay at both hotels, and expect to spend a few hours on phone/emails with reps trying to fix this with the likely outcome that you will choose the points and nights from the 7 night stay

Interestingly if points earning is your main aim then #2 is best, as you'd get more points from both hotels, but unfortunately this comes at the price of spending more! Option #1 is clearly the cheapest option (that I would probably take at this point, lots of chances this year to try other hotels for good prices methinks). Option #4 is just going to end in another complaint thread...