I think what you're looking for can be achieved using channels. Add a channel effect (Key effect > Special > Channel value) and stretch it across your timeline where you want the other effect to be sped up. Then add 2 keys to the channel value effect, one at the start and one at the end. Leave the "From Channel" and "To Channel" values for each set to the default of 1. Then set the first key's "Channel value (%)" to 0, and the end key's value to 100.
Now we can use this channel value (which increases from 0 to 100 over the duration) to affect another effect. For example, you could add a "Oscillating effect - X to Y wave", then make it speed up over time. Add the effect, then click the little green icon to the right of Speed. Choose "BEYOND Channel", leave it at 1 (because we used channel 1 before), and set the value range at the bottom from 0 to 200. Now when you run it, the wave will speed up from 0 to 200 over the duration.