Translation of Latin to English of the word 'religio'
In Latin the word religio simply means to serve, to be bonded, to be enslaved, to be owned.
Hence and even by adding the letter 'n' to it then it still means precisely the same the same thing, i.e. by being 'religious/following a Religion then you are logically, a bonded slave, servant/owned by that which you serve.
I would say your definition is a bit embellished based on my read of the word
To re-chose, or to go over again. This is my take on it.
Yes that WAS the concept/context in which the Orator Cicero used it but later it earlier in the Roman Republic it was the context used by Marius in regards to the formation of the Roman Legions, Sulla in his bid to become Dictator of the Republic, later it was adapted and adopted by both Saturnine Priests and The Auguries of the Temple of Jupiter who gave it the context/meaning I expressed UNTIL Christianity twisted and contorted it to suit their needs.