How can I access the original files (the lowerdir) of an overlay mounted on the same location as the lowerdir?

I think you're experiencing a "shared" behavior, while you need "private". See man 8 mount:

The shared subtrees operations.
Since Linux 2.6.15 it is possible to mark a mount and its submounts as shared, private, slave or unbindable. A shared mount provides ability to create mirrors of that mount such that mounts and umounts within any of the mirrors propagate to the other mirror. […] A private mount carries no propagation abilities. […]

Solution: after mount --bind … and before mount -t overlay … invoke:

sudo mount --make-private /home/username/Store/Orig/usr