Both of these areas will reduce looseness to some degree.....the damper spring is designed to keep the pinion down against the rack and this will make a bigger difference. As with anything in steering, both need to be good.
The area of steering rack-wear that has been most common in my Spridgets is the ball-end housing (the part that hold the tie rods onto the rack).....there are shims under the housing to adjust for any looseness in this area.
I know you've mentioned other repairs (such as new tie-rod ends): Is the clamp that hold the steering column shaft to the rack tight? Is your steering wheel loose? Newer cars (not sure about '71) , with the collapsable feature, can have looseness in the "collapse mechanism" (behind the dash).