Scottmel, I think I know what you mean, I myself have had knee surgeries as results of torn cartilage and was in a accident with a fractured hip. All this seems to affect my lower back, especially when sitting for a long time. I find that my posture and keeping a good posture when sitting helps more than anything.
I suggest is first understand what your best seat depth should be; measure from the inside of your knee to your back while your sitting in a good posture. This should give you a basic starting point to work from. Best to have the seats and back pillow in foam encased inside a envelope or wrapped that has no more than 3/4" thickness of polyester fiber or memory foam around the foam. The seat foam should be a HR foam 2.0 or higher density and a ILD of 28 - 32. This is a standard Firm seat that will remain the same firmness for many years. The back cushions should have no less than 1.8 density and 18- 22 ILD. A tight back sofa is fine too if you can find the one with the right depth to your size. A pillow back will allow for a easier adjustment for the manufacturer.
I think your best option is to find a custom built sofa to fit your requirements. One that offers a number of choices for seating comfort ie: a firmer seat.

Of course I built my own sofa specifically for my hips and knees, well because I am the owner of a upholstery plant.

Thank you so much for the awesome detailed response!!

I purchased the Paramount sofa from Ethan Allen a few months ago. My husband had a knee replacement a year ago and I have a bad back. The sofa is senior friendly. The height of the seat and firmness of the seat and back cushions makes it easy to get up without putting a strain on your joints. I was able to select the firmness I wanted. I am very pleased with my purchase.

Scottmel rmanbike gave a very good review of cushions and cushion reguirements. Most better end manufacturers of upholstered furniture do offer or will special order cushion options to suit your requirements.

The firmest sofa I ever had was a sleeper. I was like sitting on a board (in a good way). We've gone through our last two sofas with no luck in finding the firmness we need. The first was a lovely Drexel-Heritage that found its way into the formal living room after a week. Even though it had a tight-back, the bench seat wasn't working for us. Last one was a King Hickory and its fabric went to h*ll in a hurry and is not high enough for my 6'4" DH.