Hi Cortland,
IMHO, I don't think you need to worry about landing with a castering nose wheel that somehow might turn out of track with the direction of your landing track.
Because your specific nose wheel axle and center of mass of the wheel assembly is behind the vertical turning point during ground operations, the wheel will track true and straight in a forward direction. During the flair before landing, the nose wheel will keep itself centered and inline with the keel because the vertical line that runs through the vertical swivel point is tilted back allowing gravity to center the nose wheel. The next time you're at the market, take your shopping cart, lift the nose up and watch how the two nose wheels automatically center. The action and physics apply. Take the same cart, lift the nose and walk forward. Then while in forward motion, lower the nose and as soon as the wheels contact the floor, see if the cart turns in one direction.
As far as the centering springs, most aircraft that I know of that have castering nosewheels and use differential braking don't have centering springs. The nose wheels are allowed to caster 360 degrees like a shopping cart. The Grumman Tiger is one aircraft that I can think of off the cuff that has the previous mentioned nose wheel set up, and it works very well. The benefit of using differential braking steering is for very small turning radius. One can lock up one main wheel by stepping on that brake and pivot around the same. If there is a swivel stop on the nosewheel assembly, then one could not pivot effectively around that one locked up wheel.
Come to think of it now, Vance's Predator Gyroplane also has a full swiveling nosewheel and differental braking. He should comment on his experiences too.
Wayne