Trying to Animate Illustrator Logo in After Effects, Continuously Rasterize Not Working Properly

Let me start by saying I'm a total newbie to After Effects and am unfamiliar with all of the jargon/terminology of the field, so I will do my best to express the issue in a way that makes sense.

I have no doubt I'm doing something wrong and that the program is working just fine, but I'm having trouble with Continuously Rasterize and maintaining the crispness of my Illustrator image. I'm trying to animate a Production Compnay Logo I made in Illustrator, mainly for the purpose of putting it in front of my short films. I'm only working with 4 Layers, but whenever I select the Continuously Rasterize option in my Timeline (like I saw in various YouTube videos gauged towards my problem), it lessens the blurriness of my Logo, but is still visibly pixelated when I try to Magnify the image. My process for importing the ai file has been importing it as Footage with Merged Layers, then dragging it into the Timeline area, where I right click "Create" then "Convert to Layered Comp", then double click the to open up the 4 Layers within my ai, and copy and paste them into the main Composition. After this, I click on all of the Continuously Rasterize boxes, but then my probelm occurs. If there's something I'm doing incorrectly, not doing at all, or anything in between, please let me know.