Whichever etymology we go with: (1) relego (“choose, gather”) or (2) religō ("bind, moor") we have nothing inherently objectionable. Having chosen Epicurean philosophy, I have gathered my focus toward it and moored myself in the philosophy. It this sense it is no trouble for me to say that my "my religion is Epicureanism." But as you know, that wording is more poetic than exact (I re-read your "On '-Isms' and Pleasure Wisdom" article last night, very good!)
I do agree that it does not benefit us to throw away terms because they are misused by others. If we throw out 'god' because others have used the term incorrectly, we have let them win the argument. I think Epicurus would agree that we should not throw out the word 'religion' -- but clearly it comes with its own baggage.
We do have Religio as a bad word in Lucretius, his "oppréssa grávī sub rêligiône" (pressed down underneath heavy religion), "sǽpius ílla Rēlígiō péperit scelerôsá atque ímpia fácta" (more often Religion produces wicked and ungodly acts), etc.
Nevertheless, we understand, as Lucretius often stated, that the supernatural claims are the problem of 'religion,' not our human desire to gather a tradition and stick to it.