"If an aethiest or non-Christian were among the signers, wouldn't they have asked for a more generic, non-Christian date in the document?"
Had they asked, do you think the majority would have bowed down to their demands as they do today? I think not. I dare say he would have probably been dismissed from the meeting. Knowing how serious our fathers were about having God's help in the design of our country, they would not have wanted an aetheist in their presence.
So now we have 'Common Era (C.E.) and 'Before Common Era (B.C.E.)' as designators. Next thing you know, they'll want to change it to 'Uncommon Era', or 'Mohammed Era,' or 'Rev. Moon Era.'