Hi megadad4ever,
Welcome to the Mattress Forum! 
You’re welcome.
The good news is that you’re considering products using higher quality and durable componentry, and as you may be aware, SleepEZ and Dreamfoam are members of this site which means that I think very highly of them and that I believe that they compete well with the best in the industry in terms of their quality, value, service, knowledge, and transparency. They are extremely knowledgeable about latex and different configurations, and I would not hesitate to recommend them for your consideration.
On the Deamfoam Aloe Alexis mattress, the core of 2.17 lb is polyfoam, and I’m not sure what the “BB” means as well, unless it was referencing that Brooklyn Bedding makes this mattress for Dreamfoam.
As for the difference between a three and four layer design (each layer 3" thick), most people would tell you that you could certainly feel the difference in the products. Of course, this would vary upon the layers being used in each mattress and individual sensitivities.
The main benefit of a thicker latex mattress (or any mattress that uses similar materials) is that it can be more adaptable for heavier weights and multiple sleeping positions. It will compress from softer to firmer more gradually which means that there is more “range” of compression without the mattress becoming too firm for heavier weights (or parts of the body). A thicker mattress can also be part of a specific design that requires it such as some types of zoning or layering that needs more layers to accomplish the design goal of the mattress. It can even just be a matter of preference rather than “need”. As a side sleeper and over 200 pounds, it may be something that you find preferable.
In the large majority of cases … 8" - 9" of latex is usually easily enough to include the combination softer layers (or sometimes sections) for pressure relief and firmer layers for support that most people of average or even higher weights would need. In some cases … lighter weights or people that sleep in “flatter” sleeping positions, have slimmer less curvy body types, or who prefer a firmer mattress will do well with even 6" even though there is less “room” to design in different layers in the mattress. People that have much higher body weights or larger body types may choose more than the “average” thickness and may prefer the feel and extra adaptability of say 12" of latex. Thicker mattresses can also use firmer materials because thickness and softness are very related and work together. These are all good questions to ask the manufacturer or retailer of a mattress so they can discuss the differences between the different options they have available in terms that are more specific to the layers they use or options they provide.
One other benefit of a thicker mattresses that have multiple layers that can be rearranged or exchanged is that there are more layering combinations possible for changing and fine tuning the performance and feel of the mattress but in many cases this wouldn’t be necessary and in some cases can lead to a level of complexity that can make predicting how the layers interact more difficult (see post #2 here).
So the overall thickness of a mattress that is either “needed” or “preferred” would depend on the combinations of the layers and components that are needed to achieve the design goal of the mattress and provide the PPP (Pressure relief, Posture and alignment, and Personal preferences) that can best match each person and their unique body type, sleeping positions, and preferences.
I think that most people would generally be able to tell the difference between a polyfoam core and the all latex core as you’ve described, but that doesn’t mean that one would necessarily be more to your liking than the other. The only way to tell would be through your own personal testing. A latex support core is more durable, more resilient, more elastic, more adaptable to different weights and shapes and sleeping positions, more supportive (it has a higher compression modulus so it gets firmer faster with compression), more “natural”, and has a different more “springy” and responsive feel than polyfoam. It is a higher performance material. Of course, it is also more expensive than a polyfoam core and for some people … a latex hybrid which has the benefits and “feel” of latex in the upper layers (the top 3" - 6" which are the most subject to wear and tear and contribute more to the overall “feel” of a mattress) is worth the cost tradeoff. For others, it isn’t. All of this though is to make clear that they are not comparable in overall performance terms even though a hybrid like the Ultimate Dreams is a good quality product.
While price is certainly important, there is more about the 3 most important parts of the “value” of a mattress purchase in post #13 here which can help you make more meaningful quality/value comparisons between mattresses in terms of suitability (how well you will sleep), durability (how long you will sleep well), and the overall value of a mattress compared to your other finalists based on suitability, durability, and all the other parts of your personal value equation that are most important to you (including the price of course and the options you have available after a purchase if your choice doesn’t turn out as well as you hoped for).
Whatever you choose, you’ll certainly want to be sure that the materials within the mattress are durable in order to provide a consistent comfort life and reliable restoration. The three choices you’re listing certainly should provide comfort for the time frame you’ve specified.
If you have other more specific questions, I’ll do my best to answer them. Regardless of what you decide to do, I would be sure to consult in a phone call with the manufacturer for assistance in the comfort layers to create what they feel will be an appropriate combination for your specific needs.
Phoenix