Just curious why does this movement have 2 day wheel configuration? This one is installed under the brass plate ?
I'm going to refer to your daywheel as an overlay to differentiate it from the original daywheel, and because it is "overlaid" (glued) onto an original daywheel hub.
Just like many of our ETA rep movements need a datewheel overlay to provide Rolex fonts to the left shifted Rolex dial window position, you have been provided a daywheel overlay with fonts that are supposed to fit your Rolex day window position. Note the difference between the spacing on the original daywheel versus your daywheel overlay.
The original daywheel is not installed under the brass hub. The day fonts and white ring are either glued on top of the one piece brass daywheel's outer perimeter beyond its spokes, or printed directly onto its outer perimeter.
Look at the spacing - perhaps most recognizable between SATURDAY to SUNDAY. I commented before that it looked like that wouldn't fit in your dial day window.
So before going any further, I would make sure that your daywheel overlay fonts WILL fit to your dial day window. Take the hands off, and position the overlay where it should go and set your dial over it. See if the fonts fit the window. You can also do this with both parts in hand though positioning can be a little more cumbersome. Just take care not to scrape up the overlay fonts on the dial underside. But if they don't fit, there's no point in proceeding any further.
If they do fit, you can actually glue the overlay back onto the brass hub of the original daywheel while it remains on the movement. Obviously this would require some extra care but so does removing and reinstalling a circlip without breaking or losing it. So choose your poison, haha.