There are many potential bottlenecks and issues that can cause long slow renders. Obvious ones like large files to be read and written, hundreds of layers and effects, not enough RAM, slow media drives, etc and some not so obvious bottlenecks which are discussed in the links above.
Depending on which version of After Effects you are using there are different options.
in both CS6 and CC native ai files can be imported and converted to Shape layers with all paths intact. From the Layer menu choose Create Shapes from Vector Layer. The individual paths can then have a stroke added which can be animated independently with Trim Paths.
In any version individual paths in Illustrator can be copied and pasted one-at-a-time on to Solid layers in After Effects. A bit tiresome but doable.