How we usually handle this is to make the text with the effect a sub comp but make it so the effect takes much much longer than you want. Then in the outer comp use enable time remapping. You still have to insert keyframes but as long as you always alter the position of the key frame you are interested in AND the final key frame (assuming you work from left to right) the original timing between the two stays intact and you can tweak to your hearts content to get time based kerning you are looking for. And because the original layer is long you have the resolution to mess about with time. Some will argue that you can do this without having a long typing effect since AE will figure it all out before outputing the frame you are looking for – true in most cases but with the typeing effect it screws up previously revealed text just like you have found when trying to do it right on the layer.
Remember to turn on the little sun icon to keep the vector of the nesterd text layer nice and crisp if you resize things.
There’s another way too if your penmanship is good.
Use a brush and paint on a stroke over time on top of a precomped layer of text. This will record in real time and you can speed up and slow down as you see fit and then tweak the final performance. Use the painted stroke as a mask to reveal the text through. The only issue with this one is that you will see bits of the text yet to be revealed where the text line surrounds counters like a lower case e.