Sync Video to Audio, then Export via Media Encoder

Based on my current research, I have a feeling I know the answer, but I have perhaps a different need so I'm going to ask my question.

While creating virtual choir type videos (can be choir or instrumental groups), I must sychronize every submitted video to my master guide track. This is hugely important because all the audio for the mix needs to match, and then all the videos in the Premiere project need to match the final mix as well as each other.

I have wonderful audio softwaree DAWs that handle this very well with the precision I need, but, the video export is slow. Not horrible, but multiply 3-5 minutes times 40-60+ videos and that becomes a significant portion of the work.

So, I got a little excited when I realized that Audition can export through Media Encoder! I lined up my tracks, clicked on the export to Media Encoder, and boom, M.E., using my wonderful GPU, did its thing in about 30 seconds! I was so excited!

But. Although Audition plays the sync in the project, it only encodes the audio correctly. The video simply encodes from the beginning, making the entire excerise useless.

My question: Why can't Audition->Media Encoder do this for me? Or, does it and I just don't know what to click on? Many other Audio DAWs do this very well, but they don't utilize the GPU for the speed.

Thank you for reading and for any advice you may have.

~Jeff

[Mod note: Post moved to potentially more appropriate forum]