I'm not a shock expert but I think some things need to be cleared up
1. Springs hold the vehicle up. You make the springs just stiff enough to hold the vehicle at the desired ride height and in the case of a leaf spring the desired free arch. SO I could take a truck that applies 1000# of force on each corner and put a 100lb/in spring on it and the springs would compress 10" just to hold up the weight of the vehicle. OR I could put springs on it that have a 500lb/in rate and the spring would compress 2" to hold up the vehicle.
In this example the same vehicle is using two entirely different spring rates and will have two totally different ride qualities, Just from springs. Neither one of these are technically wrong depending on what you are after. Cadillac or dump truck basically, and thus I would argue that spring rate is extremely important to ride quality but at the same time it's an arbitrary number that is somewhat unimportant if used to relate to ride quality alone. I.e. a fully loaded dump-truck doesn't ride terrible bad even though it has a really big spring rate.
Let's ignore inner leaf friction, bushing friction etc and just say that the spring rate is the spring rate no matter what.
2. Shocks can't change spring rate. A shock is simply a fluid filled container that has some air pressure and a metering system (valving) to adjust how fast that fluid can flow out of or into the container. The motion of the axle is what fills or empties the container.
BUT
A shock does effect the rate at which the axle and thus the spring is moving depending on how fast the container is being filled or emptied through a certain size valve. Look at shock valving like a carburetor jet. In order to put enough fuel into a big engine at 7psi fuel pressure you install a big jet(s), or for a small engine you install a little jet(s).
Let's say that now you want to take that little jet and make it flow enough fuel for the big engine, 7psi is nothing so you up the pressure to get more flow but at some point no matter how high that pressure is that little jet will only flow so much fuel (think fuel injectors). Basically any size valve, jet, valving etc has a limitation as to how much fluid can flow through it, there are factors that play into this like viscosity, temp etc but I can't really speak that well about those factors..
Back to the shock, the low pressure fuel example is what is happening with a shock during low speed street driving, not a lot of motion and that motion is slow so the fluid has very little pressure on it and flows through the valving easily. Little restriction here means that there is very little or no damping going on.
Now take that same shock and drive really fast over big bumps, now it has extreme pressure on the fluid but only so much can make it through the set size valve at once (think carb. jet example) this is what makes the shock work and it is now damping the ride. How much damping depends on the vavle size, fluid velocity etc.
Now for shock terminology:
Rebound is when the shock is getting longer, the axle is getting farther away from the vehicle, going to droop.
Compression is when the shock is getting shorter, the axle is getting closer to the vehicle, moving towards full stuff.
The piston is where the valving is, this also separates the "two sides" of the shock. There is essentially an oil/fluid reservoir on each side of the piston. As the piston moves the reservoirs get bigger or smaller and the oil/fluid has to flow through the piston and thus valving which creates the damping effect.
Then you have the body of the shock, shock shaft and some spacers, seals etc.
Every shock has rebound and compression valving. Typically there will be less rebound valving than compression valving. More to come on that later.
So how does a shock effect ride quality if it can't change spring rate, well for me it's easiest to look at it as a Force sensing spring. I KNOW IT'S NOT A SPRING. but bear with me.
So I can take shock (force sensing spring) and (pretend there is no air pressure in it) and barely push on it and it compress, barely pull on it and it rebounds. Not a lot of force is put into it so it doesn't put a lot of force back. Now pretend that I instantaneously try to compress the shock, given the fact that is has a certain sized valve stack in it it can't instantaneously compress and it resists the force/damps it. If the shock was mounted to the vehicle once the instant force was applied the first thing that would happen is the shock would start working (compressing). But once the valving "packed" up (meaning it can't flow anymore fluid any faster) the force has to go somewhere and that would be into the chassis of the vehicle and thus your ass. This is what tells you ride quality. AND makes you think that the shock is changing the "spring rate", it's not but at the same time it makes it instantaneously stiffer, however it can't remain stiffer cause it a fluid connection and the fluid is allowed to flow.
Same thing would go for rebound. Only when the valving "packs" up it pulls the vehicle down, and you kind of have a set factor for rebound. Meaning the spring rate, axle weight, wheel and tire rate are all that you have going for you in rebound. These things are set and known variables. Thus rebound valving is lighter than compression valving "typically"
So how does a shock with a set valve feel different with speed and spring rate?
Shock shaft velocity.
A shaft velocity of 5"/s and a shaft velocity of 300"/s will create a totally different feel with the same valving because the shaft created pressure on the fluid through the piston and valving. Shock shaft velocities can be roughly related to vehicle speeds to the sake of this conversation.
Drive faster and hit bigger bumps the shaft velocity will be higher than cruising through the mall and thus rides different, by putting different demands on the valving via fluid pressure.
This is just a long winded brief skimming of shocks. There is a reason that race teams spend countless hours tuning suspensions. Spring rate, speed, terrain, driver preference and more all have an effect on what the shock valving needs to be.
Now for the average joe, you can bolt on a set of bilstein shocks and be realistically happy. But then there are others that won't be, to those guys go buy a set of good rebuild-able shocks, learn them and spend time tuning and changing valving.
Did that help or confuse
Oh ya. the op shocks could just be too short OR mounted in a way that they are near full extension and thus the feeling of pulling the vehicle down.