Hi kmark,
Post #1 here and the two posts it links to in the second paragraph have much more information about the different types of support system (foundation, box spring, platform bed etc) that are generally suitable for different types of mattresses.
Original Mattress Factory is one of the few manufacturers that use a box spring that has flex in it (vs a solid non flexing foundation) with their foam mattresses so if you do decide to purchase this and have tested it with the box spring under the mattress then I would use the box spring that you test it with because a solid foundation that doesn’t flex (which most manufacturers use with foam mattresses) can change the feel and performance of the mattress. If you are planning to use it on a non flexing support surface then I would ask them to move the mattress to an adjustable bed that also has a non flexing support surface when you test it so you can test it with a similar support surface to the one you plan to use.
I would make sure that any support system you use under a mattress is suitable for the mattress and in the case of latex I would make sure that the distance between the slats was no more than about 3" or less.
I also don’t see the specifics of the support surface of either the RoomandBoard Hudson bed or the Woodrow queen beds that you linked so I would make sure you know before you buy either of them.
Phoenix