When composing or arranging, what methods can be exploited to affect the listener's perception of the speed they are moving through time?
Slow down or increase in tempo. That's an effective way to do it.
Change time division. E.g. when playing quarter notes, switching to eight notes will feel faster, while switsching to half notes will feel slower, though the tempo remains the same.
Change accentuation. The standard accents are on "1" in 4/4, i.e. emphasizing each 4th quarter note. But, like drummers do, you can emphasize each 5th, 6th and so on to overlay a slower varying pattern. Or emphasize every 3rd or 2nd to overlay a faster one. Consider subdivision of quarter notes as well for more granularity. Consider asymmetric pattern overlays, like 3-3-2 (8), or 3-2-3 (8) or 2-3-2 (7), which also change the period of repetiton.