Drag your low res logo on to the new comp button, making a new comp with the size & aspect of your small logo(Precomp Logo).
In your animation. Precomp each layer, checking the "leave all attributes" box.
Import new larger res version and bring it into "Precomp Logo". Lower the opacity to 50% and eyeball/scale it to match the size of the small logo. If the anchor points are the same, or you know that it's 2x the size this will be easy. Once you have it matched, bring the opacity back to 100 & delete low res version.
Select each of the precomp layers in your main animation, select "Precomp Logo" from your project window, hold down alt and drop on one of the layers. Should change all your layers to the new precomp. Now just use the "collapse layers/continuously rasterize" button and scale up to your hearts content.
Just as an alternative to eyeballing or using opacity to line up the two logo versions, you could use the Difference blending mode on the top one ... when the screen goes black, they're exactly lined up.