Did you even price it out? I just checked the same dates in Oct, Hotel 31, with a private bath (yes they offer shared bathrooms) for two people, three nights is $547.
The Sheraton Manhattan was less.
I don't know how you're coming up with your rates...
Hotel31.com check in Oct 20th and check out Oct 25th - 170 per room for 1 person with private bath.
spg.com Sheraton Manhattan check in Oct 20th and check out Oct 25th - 477 per night.
Do you know of some special discount for Sheraton Manhattan? The cheapest rate I can find for Sheraton Manhattan is 317 per night from Sept 27th to Oct 2nd.