Couple of thoughts here. A smaller cylinder will respond faster than a larger one. But, you seem to be using the most common size, so I suspect that is a dead end.
The bigger the holes and lines, the faster the fluid can flow, which will make the cylinder respond better, but due to the nature of the system, you can't really get too much volume.
Not enough is a problem, the control valve in the steering sector supposed to control how much is sent, not the lines.
The whole setup hinges on the steering sector. Think about how it works. As you are driving straight, the spool valve is closed, sending no fluid to either the ram or the regular steering assist part.
When you start to turn the steering wheel, it tries to turn the pitman arm through a spring hooked to the spool valve.
If the arm moves, the spool valve stays centered and no fluid flows.
Of course, unless the arm is unhooked from the steering, it is not going to move. When you continue to turn the wheel, the stalled arm moves the valve against the spring tension, and the fluid flows adding assist.
If the assist is not enough, the valve moves farther and more fluid flows.
As the arm moves, catching up to the input, the valve centers and the fluid stops. The arm "chases" the input.
Now, what this means, is that the output arm is the feedback sensor for the whole system.
The steering box does not know or care what the hydraulic cylinder is doing. It only cares about what the output shaft is doing.
If you disconnected the pitman arm from the steering, and put a load on it, the cylinder would move to the end of its travel and stay there under pressure until the arm was centered in respect to the spool valve.
Which means, any slop between the old steering arm and the steering is going to cause the cylinder to over react.
It sounds to me like the cylinder is pushing part of the steering faster than the arm is moving.
Or, there is damage in the steering box that is causing the spool valve to float and not react to the output like it should.
I hope all that made sense, my leg is hurting and it takes my mind off it when I do the whole logical chain of events thing, plus I am running on too little sleep.