Brew,
Not to be nit picky, but those end caps don't actually "slide" on to the mounting brackets. Instead, they are made to "snap" onto the mounting bracket once they are properly positioned.
I don't have a photo of the back of an end cap, but the ones on my '70s had a small spring steel catch that clamped onto the outer edges and the inside end of the mounting bracket to keep them from sliding back off the end of the strap/bracket when in use. It sure looks like they should slide onto the side rails of those mounting brackets but they actually have to be positioned over the mounting bracket and snapped into place.
I encountered one end cap that would slide a bit on the bracket and discovered that the end of the spring steel clamp and been broken off, likely by trying to slide it into position on the bracket.
I found that it was easy to remove them by simply snapping them off the bracket with a flat blade screwdriver (as shown in the attached photo) so replacing them just reverses that process. Good luck.