Hi tennisman,
Quilting will “pre compress” the foam and make it firmer than it would otherwise be yes. Different types of memory foam of the same density will also have different properties as you can see in post #9 here and post #8 here. Density is the main factor of quality and durability but different memory foam versions of the same density can have different properties.
As an example … the tempurpedic 8 lb memory foam is actually softer feeling than their 5 lb memory foam and also more conforming while their 4 lb memory foam is softer than both but also less conforming than both. memory foam is also quite tricky because it responds to pressure as well as heat, humidity, and time it is compresses (it relaxes over time) while faster response foams respond mainly to pressure alone.
It’s quite possible that a simple stretch cover could make a difference but there are also other factors that could play a role as well including what is under your mattress, what is over your mattress (mattress protector, sheets, and bedding) and the temperature of your room. Post #6 here and post #2 here and post #6 here and post #2 here about “fine tuning” may also be helpful to help you identify the “cause” behind your symptoms.
Phoenix