Sometimes it's easy to be both right and wrong, especially on Islam.
According to Anjem Choudary, Islam is not so much a religion as a dee, which is a complete way of life; many if not most imams agree with this, which makes you right although perhaps not how you meant. Unfortunately there are many people around that if they dislike someone, for example Anjem Choudary, will diss everything that person says or does; mostly these are non-Muslims that know about Islam only what they couldn't avoid picking up from whichever leader or celebrity plies them with false narratives whilst telling them how clever they are.
I am no politician or scholar, so I would guess even if there is something in what you suggest about changing the wording there are many reasons why the proposal could not work with Islam. Just one powerful reason is that while westerners accept separation of church as an ideal to accomplish or at least strive towards, such separation will always be utterly rejected by Islam because the church is the state and therefore one simply could not survive without the other.
Bear with me for one paragraph that may appear off topic: Most westerners find it difficult to grasp that jihad is the heart and soul of Sharia, not as an aberration but the essence without which Islam could not exist. Non-Muslim beliefs, even atheism, are anathema to Islam, and the goal of jihad is not to knock down buildings and blow people up but to bring every living human under the rule of Sharia, Islamic law, using any and all means. Nothing can change as long as Islam exists, yet well into the Third Jihad few westerners understand this and still talk about reforming Islam towards living in harmony with other faiths.They are not free however to demand political changes based on the ramblings of a 2000 year-old or 1400 year-old so called prophet.
And here is where everything you said falls down, by using logic and what sounds reasonable to a westerner, and expecting or hoping that it makes sense to everyone. In this respect I can understand what you say from both sides, Muslim and westerner, though sometimes I wonder if that's an advantage or an obstruction.