While you find my definition of religion too narrow, I find your definition too broad.
Your definition encompasses each and every single factor an individual will live their life by, whether by choice or not, thus you're effectively defining the act of being alive as being involved in a religion.
My definition of religion requires the individual to worship an entity, be it supreme or human, and to live their lives governed by the rules that this entity defines or dictates.
Your point about your believing in God but not being a member of a formal religion aligns with my definition of not being religious. If any individual accused you of being religious without cause it would be self serving, regardless of how they identify with their own beliefs. By categorising you it allows them to stereo type and debate you based on that stereo type.
The issue you have though is that by your own definition you are religious, so any accusations are justified. The problem now is that because you don't identify with any particular religion the discussion is doomed to fall into disarray as there is no common ground of understanding around which to debate. The question now becomes, if you really are religious, which religion do you follow? If you can't answer that, then you're not religious.
Your arguments are logical. We have determined that our differences essentially amount to a difference in how we define religion. Mine is broader yours more narrow. Now we need to determine which is more useful more or functional if you will. You are of course correct that according to my definition I am essentially defining the acting of being alive as being involved in a religion. That is intentional for it is both accurate and instructive. Action is unavoidable and ultimately their are either subconscious or conscious reasons for these actions.
Lets examine the functionality of your definition. Lets use my case as an instructive example.
You ask me which religion do I follow. That's easy I follow the religion of Ethical Monotheism.
Ethical monotheism is the belief:
A) that there is only one God (monotheism)
and
B) that He is the source of ethics and morality.
https://en.wikipedia.org/wiki/Ethical_monotheismNow lets apply your criteria from immediately up-thread.
1) Is there a defined set of rules that I have to live by? Yes I have to believe in God and I have to figure out the ethics and morality that can be logically derived from a belief in God and follow those too.
2) Is there specific place and time I need to worship. Yes everywhere and always through my actions.
3) Is there an specific entity I need to worship? Yes God.
So according to your criteria as stated do I have all of the defining elements of a religion? Am I am religious?
If you answer no then you are essentially taking the position that someone who has embraced a religious construct to such a degree that it utterly transforms ones behavior, beliefs, and ethics is not religious. You can take that position but it exposes the overly narrow boundaries of your definition.
If you answer yes then you are essentially making the case that taking the logical position that consists of two claims A & B above is religious the the converse the logical position of not A not not B is not religious. This dichotomy begs further explanation.
I would argue that a broader definition of religion such as the one I outlined is more functional as it can be used to broadly capture the actual motivations of human action and behavior. It allows for an apples to apples comparison if you will of human belief structure.