Hi CMay and welcome to the Mattress Underground 
I have been searching for a mattress for a while, and the more I research, the more confusing it is to choose. I also came across concerns about the reputation of the companies and sagging beds issues
It’s not uncommon to fall into ‘analysis paralysis’ searching for a mattress…so many options and everyone advertising ‘the BEST mattress’ for this or that type of sleeper. Best to keep the basics in mind: any mattress you choose will be will be based on your Stats (height, BMI, sleeping position(s) and any underlying health concerns) and your PPP (Posture and alignment, Pressure relief, and Personal preferences). No one can tell you what bed will work for you - besides you!
I had a medical procedure that required me to remain in a compromised position for many hours. There are problems with my neck, hips, lower back, and legs. I am 130 pounds and a back & side sleeper.
Sorry to hear about the recovery from the medical procedure! It sounds like this is adding to your existing aches and pains…you may want to ‘soft reset’ the mattress search; If you have not already, you may want to take a look at the Mattress Shopping Tutorial to see how to find a good retailer/manufacturer, as well as the Mattress Specifications You Need To Know and compare this to the Mattress Durability Guidelines to see how durable specific materials are. You say you are experiencing pain in a number of areas…does the pain occur during the night, or when you wake up? Does the pain go away during the day? You don’t say what type of mattress your current one is, so there are a few different aspects which could be contributing to the pain.
My budget is $700-$900. Trying a few hybrid mattresses at the Casper Store, I didn’t like how my lower back felt compared to all foam mattresses
think 3 inches of memory foam or engineered foam (that feels like it’s between memory foam and latex?) on top are most desirable. Soft-medium, 5-6 ? Pressure relief, weight, and no fiberglass are the main concerns. After opening my old mattress with fiberglass, I developed chronic urticaria
Again, I cannot say for sure what is the best construction that is good for your PPP as it would be just theory at a distance and not based on your particular needs and preferences. While memory foam is popular material it has some draw backs but if you choose the correct density and firmness, is a good choice for pressure point relief. In general, any foam in a potential mattress should have no more than an inch or so of lower grade foams (for memory foam no lower than 4 lbs/cuft for normal range weights, and 5lbs/cuft for higher range weights) and if polyfoam is used, with at least 1.8 lbs/cuft density. From the partial Stats you gave, your weight, I am assuming that you have a lower BMI, so don’t necessarily need more than 1.8 lbs/cuft for a polyfoam base layer as long as it provides support to keep your spine in neutral alignment in all your sleeping positions and lend some comfort to the uppermost mattress layer. Unlike latex, memory foam firmness is not directly correlated to density: you can have a high density ‘plush’ comfort level, or a firmer layer of lower density.
I have checked many brands and narrowed them down to Nest Quail, Novosbed Soft, Zoma, Leesa Original, Dreamfoam Essential, and Douglas. Is there anything else I should check?
You did not state the size of the bed you are looking to get but for lower bed sizes, you should be able to find a quality mattress in the neighborhood of your budget, though many of the mattresses you listed are typical ‘big brands’ in that they are not transparent with the densities and composition of their components, which makes it difficult to assess how long they are likely to last and maintain their initial properties and if they would fit your body profile. There are options in your budget range. You mentioned the Nest Quail Nest Bedding is one of the Trusted Members of the site and the Quail is a good quality memory foam mattress with 3" of 2.8 lbs/cuft Energex foam in the comfort layer, 1" airflow layer and 6" of 1.8 lbs/cuft base foam with edge support, Which is available in medium and firm comfort levels, and the sale through the end of February puts it within your price range. Many of the Trusted Members offer foam and foam hybrid mattresses you may want to look into before you make a decision.
I was reading about DIY. What do you think about getting a 5’’ base, 2’’ latex foam as a transition layer, and 3’’ memory foam for the top? Is it too risky?
Base 5" HD36-HQ or LUX-HQ Foam https://www.foambymail.com/foam-mattresses.html
Transition layer 2": Pure Green Natural Latex Mattress Topper | SleepOnLatex.com (Medium or firm?)
Top layer 3": Sorry, I can’t have more than 2 links. It’s either 3LB ViscoSAVER , The 4LB ViscoPLUSH , or 5LB ViscoMAX from foambymail.
A DIY Mattress can be ultimately rewarding in allowing maximum customization to your body and preferences - as long as you are willing to take the time to learn mattress basics, and energy to rearrange, exchange, and return layers that don’t work, You’d also need to keep track of the exchange and return policies beforehand so you are not stuck with foam layers you can’t use. The base layer is very firm and will be supportive; a transition layer of latex would provide a breathable durable layer which you might look at the medium firm comfort level, and for the top memory foam layer, I’d go either with the 4 or 5 lbs to ensure durability and that the foam will not break down in 6 months or so, but…for firmness that is a bit more complicated because all layers work together and if you make a change to one layer than you have to adjust other layers accordingly. All in in all that’s dependent on your preferences but especially on your needs as you are experiencing various pains…whether you want to sleep on a very firm mattress, or prefer some ‘give’ to it.
I’d say that unless you are ready for a steep learning curve, working with an experienced and knowledgeable manufacturer or retailer to help you select a good construction would be your best bet….For this you may want to have a look at the Trusted Members like APM, DIY Mattress and DIY Natural Bedding, that offer components for DIY.
Make sure to make note of any shipping/exchange costs to keep within your budget. While the separate components prices can save you some money, - if the DIY doesn’t feel correct, you’ll need to make adjustments and may cost more in the long run.
~ Basilio