Honestly, I would probably just bond it in the right location and call it a day(strong epoxy) . That rubber piece just acts as a spherical joint allowing the shaft to change axis without binding. The reason it failed as you can spot by the polished surfaces is micro compression cracks. Porsche lower control arms are also notorious for that. Its when the loading and unloading especially in compression creates tiny cracks that get bigger and bigger with time. I know Aluminium is a different material, but it is the easiest one to spot.
That is why when you sprayed lubricant it stopped making noise. The rubber surfaces stopped working against each other vs stretching as you were theorizing.
As long as the rest of the rubber looks good, go ahead and glue them back together and enjoy the cheap fix.