Losing quality from AE import to Premiere

I have a simple title animation that I made in AE, to add to my Premiere project.  The quality is perfect in AE.  It's also perfect in the output file (Quicktime RGB + Alpha).

However, as soon as I import the file into Premiere, the quality goes out the window.

I thought at first it might be due to the framerate difference (Premiere comp is 60, AE comp was 30).  So I recreated the AE animation at 60 fps, but that didn't make a difference.  The resolution is the same between both files (3840x2160).

I also attempted to add an adjustment layer to my Premiere file and use it as a dynamic link to AE, where I recreated the animation again in the new linked file.  I figured that the AE comp would inheret the comp settings from Peremier.  That made no difference.

The only method that worked is if I imported the file into a brand new Premiere composition and used the AE comp settings to create the Premiere comp.  Then it rendered in its full quality.  However, I'm sure that if I recreate my Premiere project in this new file, that my video will be out of sync with the comp settings of the AE file.  Hopefully that makes sense.

How can I combine my AE animation with my Premiere project video without losing any quality?  I attached a few images.  One of them is what the quality looks like in Premiere.  The other is what the quality looks like in the rendered AE file.

I know it has something to do with the composition settings between the 2 files, but I don't know how to marry the two together.

Any help would be greatly appreciated.