In the Milky Way Project I already found fast movers, I called them Pure Green Stars, because they look like green stars in the MWP 3.0.
For one of them I even calculated the speed on the sky: ~34.2 arcseconds per hour. Here is the object, moving between two images taken 10 minutes apart:
But spitzer does take images even now. I picked two images of 3.6 µm wavelength. The first taken between 2004-10-07 08:00:01 and 2004-10-07 09:05:24. The second image was taken between 2017-01-03 09:24:25 and 2017-01-03 11:09:22.
So the time difference is now more than 10 years and you are able to see much slower movers.
To find movers and variable stars I used a trick: The image from 2004 and 2017 are processed exact the same, the only difference is that 2004 is green coloured and 2017 is red coloured. After matching both images everything should be yellow, like in this image:
But sometimes you see some stars that are more green or more red:
Those are variable stars. The green star was 2004 brighter and the red star is this year brighter.
The other thing you see are stars with one red side and one green side:
They move in years only a bit. They can be small or large and they are called Proper Motion stars. Proper Motion stars are not part of ours solar system.
The fast mover I showed on the top is part of our solar system, but not part of the Kuiper Belt. Today I used another timeframe. If there were faint objects, which move from one point to another, then it could have been a Kuiper Belt Object or a nearby brown dwarf.
These images are a part of the sky crowded with many stars. This shows how sensitive Spitzer is even now, more than 13 years after its launch into space.