Looks like everything is being mixed down together and you don't have the tracks properly panned/assigned, or your settings when exporting are off.
This is a great way to work with 5.1 in premiere IMO when you have 6 mono wav channels. Watch the entire thing all the way through, you'll learn some stuff, and at the start of the video he tests different things so you gotta wait till he actually shows the main method.
You won't really be able to do this without redoing your entire audio mix so just use it moving forward in future projects. For your current project, you can use the "solo" function and highlight all tracks that have relevant audio for the Left front channel, then export them together as a 24 bit mono wav channel, this will mix them all into one left channel file. Then, do the same but for the Right front channel, then for the Center, etc. The reason you'd do this is because if you export them all together it seems like things are getting messed up and mixing outside of their respective channel (as you said, your center is mixing into, left, right, front, back). You'll have 6 mono wav channels and then to arrange them into one 5.1 file you could use audacity, ffmpeg, or any other audio converter, there's probably tutorials online on how to take 6 tracks and combine them into a single 5.1 track. it is possible to find a tutorial to encode back to DTS, but I dont think im allowed to link that video here, because its not licensed. For me, I use that tutuorial vid I linked, edit the movie, export 6 wav's, then encode those 6 wavs to a DTS-HD ma track, then combine that with my video file with MKVToolNix to create my release file: an MKV with h264 video, dts audio, chapters, and subtitles all built in.
Also AAC is actually more advanced than AC3 for the sake of quality/bitrates, it's just that AC3 is more compatible and widespread which is the benefit, but in 2021 I don't think that's an issue. So in other words, AAC isn't "saving space by losing quality," it can be the same quality and bitrate (640kbps) as AC3, but since it's more advanced it takes up less space.
I don't see a point in doing a stereo track either, because nowadays basically everything is capable of playing a 5.1 mix on stereo speakers or headphones, but if you want to be sure, then you can go ahead and create one manually, mix all the lefts together and all the rights together, then put the center in both of them, but definitely adjust with the volumes to make sure the center dialogue is audible.