Hi Kbj1125,
I don’t know of any square frame but to properly support an all latex mattress the gaps between the slats need to be 3" or less. With only 4 slats it doesn’t sound like this is the case with yours and I would strongly suggest getting a foundation that would be suitable. The foundation thread here will help.
I don’t think either of these would normally be in the “best value” group unless you happened to be in Houston in which case you could test the Tranquility bed before buying it.
The first step is always Post #1 here which has all the information, guidelines, and steps you will need that can improve your odds greatly of finding the best possible quality and value mattress that is also the best “fit” for your needs and preferences. It also includes a list of some of the best quality/value online manufacturers in the country and I would certainly look closely at these before making a purchase from either of the options you are considering.
A forum search on “plushbeds” and on “tranquility” (you can just click both of these) will bring up more information about both of them.
Phoenix