Hi blaster668,
Welcome to the Mattress Forum! 
A high BMI presents special challenges and generally requires firmer materials (in the support layers especially). This could be firmer latex or innersprings (the type of support component would be a personal preference and in the right design either could be suitable) or even a zoned construction. The same overall guidelines apply with higher weights though that PPP (Posture and alignment, Pressure relief, and Personal preferences) along with using high quality durable materials that will maintain their feel and performance for longer periods of time are the way to make the best choices. Heavier people in general will need firmer and thicker comfort layers and firmer support layers than those who are lighter and because no materials will last as long with much higher weights the quality and durability of the materials and components is even more important than normal. I wouldn’t “rule out” any types of mattress and base your choices on your own personal testing. Post #3 here (which I think you may have already found) has more information and suggestions about heavier weights that is worth reading.
As a brief synopsis, higher BMI ranges will need more durable materials and components in a mattress and in a BMI range of 30 or higher I would include any 1.8 lb polyfoam or 4 lb memory foam as a “lower quality/density” material (relative to a higher BMI only) and minimize their use to a total of “about an inch or so or less” in the mattress. For polyurethane foam, if your mattress is one sided then I would look for 2.0 lb per cubic foot density or higher. If the mattress is two sided then I would use a minimum density of 1.8 lbs per cubic foot or higher. For memory foam (or gel memory foam), if your mattress is one sided then I would make sure that any memory foam is at least 5 lb per cubic foot. If the mattress is two sided then I would use a minimum density of 4 lbs per cubic foot.
As you’re aware, the lower 1.5 lb polyfoam core and the 4 lb memory foam are below what I would recommend, and unfortunately you’re finding out that the durability is shorter with your BMI and this combination of materials.
The materials, layers, and components of a sleeping system that are closer to your skin will have a bigger effect on airflow, moisture transport, and temperature regulation than materials, layers, and components that are further away from your skin and softer mattresses or foam toppers will tend to be more “insulating” and for some people can sleep warmer than firmer versions of the same material. Your current mattress has a total of 5" of memory foam, which being one of the least breathable of all foam types, and being less supportive and softer in comfort, and providing quite a bit of a “cradle” for you when you sleep, would certainly be very I insulating and potentially quite warm.
In very general terms, gel and/or other thermal conductive or phase change materials can have “some effect” on the sleeping temperature of a particular material but how much of an effect they will have and how long the effect will last will depend on the specific formulation of the material and on the “combined effect” of all the other materials and components of the sleeping system including your sheets, mattress protector, and bedding. Many thermal conductive or phase change materials tend to have a more temporary effect when you first go to sleep at night or over the first part of the night than they will over the entire course of the night. You can read more about phase change materials in post #9 here and at the end of post #4 here and you can read more about the various different types of gel foams in post #2 here.
It’s not really possible to quantify the sleeping temperature of a mattress for any particular person with any real accuracy because there are so many variables involved including the type of mattress protector and the sheets and bedding that you use (which in many cases can have just as significant an effect on sleeping temperature as the type of foam in a mattress) and on where you are in the “oven to iceberg” range and because there is no standardized testing for temperature regulation with different combinations of materials … there is more about the many variables that can affect the sleeping temperature of a mattress or sleeping system in post #2 here that can help you choose the types of materials and components that are most likely to keep you in a comfortable temperature range.
I’m not familiar with Classic Bedding, and their web site doesn’t provide any meaningful information for me to make any comments about their products. Your best course of action would be to take a trip out and visit with them and find out what they might be able to custom build for you and the quality of componentry used in those products. The 368 unit they’re mentioning sounds like the Leggett and Platt Hinge-Flex, which is a very durable innerspring unit. The foam mentioned, as you surmised, is 1.8 lb polyfoam of a firmer 35 ILD. I don’t know if there is more foam in this mattress, as 1.25" isn’t much for a comfort layer of polyfoam. And yes, I would recommend 2.0 lb or higher for the poly foam. I’d also inquire about any return/customization options when you visited just in case you purchase there and it doesn’t turn out as well as you would have hoped.
The Brooklyn Bedding Best Mattress Ever contains durable materials, and is available in Soft, Medium or Firm. You’d want to phone them before placing an order to discuss your requirements and use their recommendation of the comfort level to choose, which I believe would be the Firm for your BMI. Brooklyn Bedding is a member 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. They also offer a 120 night trial.
The Best Mattress Ever is a good option if you want to try out a mattress that is an affordable latex option, using a polyfoam core instead of being entirely made of latex. Latex will generally be your most durable foam choice, so if you like the feel of it and it falls within your budget, it certainly would be worth your consideration.
It sounds like you’ve already been reading quite a bit on the site, but just in case you missed it, I would make sure you read the mattress shopping tutorial here. Two of the most important links in the tutorial that I would especially make sure you’ve read are post #2 here which has more about the different ways to choose a suitable mattress (either locally or online) that is the best “match” for you in terms of “comfort”, firmness, and PPP that can help you assess and minimize the risks of making a choice that doesn’t turn out as well as you hoped for and post #13 here which has more about the most important parts of the “value” of a mattress purchase 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 all the 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).
I hope that information helps you out. I think you’re already on the right track and have a general idea of the types of components you need to look for in your new mattress based upon your comments. I’ll look forward to learning about your progress and of course any other questions you might have.
Phoenix