Hi thefussys,
Trying to match one mattress to another using either “specs” or “feel” is an almost impossible job because of the many variables involved. You can read more about “mattress matching” and the 3 ways that it may be possible in post #3 here and the links that it contains. As you will see … it’s much more effective to try to match any mattress you test against a common set of standards instead of against other mattresses which may not be possible to accurately replicate.
An example would be your own experience where two very different mattresses with different materials and layering feel similar to you even though they may feel very different to someone else. You may feel that another mattress is similar to both of these while someone else with a different body type, sleeping positions, or perceptions may feel it is very different. Each person is unique in how they interact with different mattresses and how they feel on a particular mattress.
Your budget is also very low for a good quality memory foam mattress (especially if you also need a foundation) and may mean that you would be looking at lower quality (lower density) materials that won’t last very long and I would tend to avoid materials such as memory foam that is lower than 4 lb density or polyfoam in the base layer that is lower than 1.8 lb density.
You are also not in a budget range that would include even most latex hybrid mattresses (a few inches of latex over a polyfoam support core) which is a more costly material than memory foam.
If you are committed to either a reasonable quality memory foam or latex hybrid mattress … I would consider raising your budget slightly so that you don’t need to buy a cheap low quality mattress that will not have the quality/durability that makes it reasonable value and have to replace it very quickly.
As a reference point … there is a list of online memory foam providers that have some of the best quality/value available in post #12 here which will give you a good sense of what a reasonable memory foam budget may be. There are some great quality/value choices here and some that are close to your budget (mattress only) but still above it.
There is also a list of some of the members of this site who sell online and are very experienced in helping their customers make suitable choices and have some of the best quality/value in the country in post #21 here. There are also some latex hybrid mattresses here which again are close (mattress only) but still above your budget.
There may also be some local factory direct manufacturers or better sleep shops in your area which have good quality/value in lower budget ranges for both memory foam and latex hybrids and if you let me know your city or zip I’d be happy to let you know of any options or possibilities I’m aware of in your area.
Phoenix