The portal will allow you to choose from available hotels. So, if rooms at Embassy Suites or Staybridge Suites are available when you open the portal, they will be on offer, along with the respective available room choices. If all those blocks have been booked and the only thing left is a King bed single at the JW Marriot, that is all you will see.
Like Hahnarama, I always book outside the portal. However, this can be considerably more expensive if you do not have the buffs that come with loyalty programs, brand credit cards, etc.
There is also a Homewood Suites downtown that has historically not participated in the housing block but has the kind of suite-style rooms you are looking for. Worth checking out.