Hi dsf,
Although latex is a very high quality material and very durable … it is also very subject to oxidative breakdown from light and ozone and other factors and requires a high quality mattress ticking to last as long as is should. A mattress cover that is so thin that you replace it twice in 10 years is not suitable for a mattress IMO … especially a latex mattress … and the brittleness of the latex is a sign that it has oxidized and is breaking down and biodegrading.
A good quality mattress ticking that fits tightly around the mattress will normally deal with this and if it does happen it’s easy to just re-arrange the latex. There are benefits to gluing the latex layers but in the eyes of many these are offset by the advantage of being able to change out layers as needed or even replace a single layer when it wears faster than the others. It seems to me that the biggest issue with the cover wasn’t the bunching but that i just wasn’t a suitable cover.
As you say … this is a “strange” problem and may be from the cover “gripping” or prematurely wearing the sheets as you say or it could be that the sheets didn’t have a deep enough pocket and were too tight. I’m not sure what kind of sheets you were using (this could be part of the issue) but this is an unusual problem and not one that I’m sure I could “nail down” without more specific information about the mattress and the sheets. It’s certainly not the norm.
I should also say though that your higher than average weight could easily contribute to both of these issues because it would both stress and wear the sheets more and in combination with the thinner cover contribute to the shifting of the latex. Your current mattress is also a lower ILD than would be the “norm” for your weight and it would allow for extra “travel” and wearing of the sheets because you would be sinking into the mattress more than average.
It may be worthwhile looking at the deeper layers of foam to see if they are also breaking down prematurely. If they are … then they would also need to be replaced but if it’s only the top layer then I would consider just replacing the top layer and buying a higher quality zip cover. It will be much more than a terry cloth cover but it will be worth it for all the reasons you mentioned.
The Ultimate Dreams has 3" of Talalay latex and the rest is high quality polyfoam so it wouldn’t have the same “value” as an all talalay latex mattress but given the condition of your mattress (or at least the top layer) almost anything would be an upgrade if the mattress is no longer suitable for sleeping on. They are a high quality manufacturer and like the other members of this site … I think very highly of them. They are among the “best of the best” in the country in terms of quality and value. If you do decide to go in this direction make sure you tell them you are a member here so you can receive your bonus (their shredded latex pillow).
The base foam they use is high quality (2.35 lbs) and very durable. The upper layers of a mattress are far more subject to wearing out and softening and base foam of this quality will normally last for 10 years or longer although again higher weights will soften or wear out foams faster. It will not have quite the same feel or performance as latex but it’s fine in terms of durability. How it performs of course in terms of support though will depend on its ILD and how it interacts with your weight. It’s a “standard” layer rather than having an adjustable firmness level like the latex layer in the mattress. Chuck will be able to give you good guidance as to how it would suit your height/weight/shape and sleeping positions and if he thinks it would be firm enough would help you choose the most appropriate comfort layer of latex (firmer would be better) that can give you the best possible combination of pressure relief and support that is possible within the range of choices they offer.
Latex is the most breathable of foams and the coolest and the upper layers are the biggest contributors to sleeping temperature but it’s only one of the factors that makes any particular mattress cool. It has a 1.5" layer of quilting foam on top so this would modify the feel of the latex a little (which the padding on your cover would also do if it has a padded or quilted layer on top) but it’s also a breathable foam that they use. Adding a wool mattress pad can also cool down a mattress as well as using different materials in your bedding so overall it’s quite likely that you will be fine in terms of heat.
Knowing the materials in a mattress makes it fairly easy to predict what the long term reviews will be like 
This is a Boyd mattress (the Natural Flex 935 which you can see here) and like you say they are very loose with their terms. Engineered latex is polyfoam that has been “engineered” (you can see the grooves) to feel a bit like latex. It has an inch of latex in it and the rest is polyfoam. They are a Chinese made mattress but to their credit at least the polyfoam has been CertiPur certified. They are often sold at liquidator outlets because their marketing terminology tends to command higher prices than they are worth (people think they’re buying a premium latex mattress). At least the price at wayfair is more reasonable. A search on Boyd (you can just click this) will bring up more posts and threads about them.
While there are many great value mattresses that are made by the members of the site (and the ones that specialize in online sales are in post #21 here), this is one of the best values in a latex/polyfoam hybrid mattress in the price range you are looking at. I would probably be looking at either this or checking your layers and adding a new top layer and a much higher quality ticking if your lower layers are still OK.
Post #2 here has some of the better options in the NYC area and post #2 here has more detailed descriptions of many of them (the last 5 would be better value for the needs and preferences of most people)
Phoenix