Some guys leave in the top spring. The pedal resistance goes back to about normal, but the shoes still self center. The most common problem is that the shoes self activate more easily without the spring. This happens either from high spots on the drum , mis aligned shoes, shoes adjusted too tight, shoe rollers not fully seating in the cradle due to interference from the cotter pin, shoes not centered, shoes not arced, adjuster arms hanging up in the bores, or some other reason a lead shoe is catching the drum. Putting the top spring in could help prevent that by inhibiting the servo activating effect. If you're using the square pins, burrs on the tracks can catch and rotate them too and hold the shoe too close to the drum..
If your adjuster arms are equal length , which is very important in either the stock Ford or Ted's system, I can't see that leaving the floating adjuster in would do anything but improve it. If they are unequal, one shoe will activate the system because its too close to the drum, or in the case of the stock system you will only have one shoe doing the work.
its usual to have to adjust the brakes looser on Ted's system until everything has seated. If they are adjusted as tight as you would on a stock system, they will self activate.