spring tension
The tension of the drive belt is controlled by a fairly gentle spring. The tension is, IMHO, just enough and any weakening of the spring over time could result in a poor spin.
Does your machine have a pump driven by the main motor, and does it spin slowly when pumping out, only ramping up to full spin speed once the drum has emptied?
If so, the spring tension is critical to these machines spinning well. When the drum is full of water, it starts pumping out and the basket revolves slowly, the gentle belt tension and the high load of trying to spin a full drum of water means that the belt slips a lot, giving a gentle rotation of the basket. As the water level drops, the load on the belt decreases and the slippage reduces, which means the spin increases. Once most of the free water is pumped away, the basket turns more easily, so the belt slippage falls to almost nothing and the the spin increases to full speed.
I think your problem is too much slippage. You need to find out why. AS a TEMPORARY test only, you can pull on the spring while it is spinning weakly, to see if spin speed picks up when you increase spring tension. Be careful not to touch anything moving or electrically live, you could get injured or killed.
DO NOT fit a stronger spring or try any other dodgy method to increase spring tension. The gentle spring tension is an essential part of the design, if you fit a strong spring, it will try to spin with the drum still full, that will either (a) create a vortex and spin water over the top of the drum, creating a flood, or (b) overload and burn out the motor.
Australian Simpson machines of the 1970s used a similar system and they had a range of holes for the tensioner spring, you could simply move the spring to a further hole to increase tension. But if I recall correctly, the Speed Queens don't have that arrangement, so I don't think you can adjust the tension.
You first need to eliminate any sign of stiffness that might limit the spin getting up to speed, and check that the pump is getting rid of the water quickly. If the pump is emptying the drum slowly, then the spin phase might be almost over by the time the drum is empty, leaving almost no time for the faster spin. So check for blockages, kinked drain hoses, and so on. If it empties into a standpipe, put the drain hose into a sink instead and watch the flow rate when pumping out, these machines really blast the water out if pumping correctly. Anything that slows the rate of emptying will affect the spin results.
If that doesn't solve your mystery, maybe the spin bearings are seizing, so the drum is hard to turn at speed.
Also check that you have the correct belt for your washer... IIRC, there are two similar belts for different Speed Queens, if you fit the larger belt you will never get enough tension. They are very similar in size but not identical.
If there is no adjustment for spring tension, replace the spring and see if that helps...
Check that the belt is threaded correctly around the tensioner - from memory the tensioner wheel runs on the BACK of the belt, not the V side of the belt.
the video linked below shows the tensioner. The camera work is pretty bad, but you get a glimpse...
