There's nothing inherent in TRs that causes them to lose effectiveness as speed reduces. What often causes this is a decision to schedule the maximum reverse thrust N1 (or EPR, for the Derby types) with speed, in order to reduce the risk of reingestion or loss of directional stability.
The spoilers, ON THEIR OWN, are probably the least useful of any of the devices, since they only create drag, which is less and less useful for stopping as the speed decreases - eventually you'd be relying on rolling friction to come to a halt. They are great for increasing the effectiveness of the brakes, by increasing the weight on the wheels, but that's really the brakes doing the work.
If you had to choose one of the three systems to leave off the plane during design, I would suggest the spoilers would lose out.