The first fallacy of your argument is that those who wrote the Constitution were modern conservatives. They weren't. They opposed the conservative King of England and taxation without representation. So that's your first fail.
I bolded the last section, because extended your arugment logically, therefore the government cannot restrict abortion in any way because they are not mandated by the Constitution to deal with this issue. The government has no right to impede, restrict, or hinder a woman's right to determine what happens to her own body.
Last but not least, nothing in the Constitution recognizes that life begins at conception. In fact, the unborn are not even mentioned, so any idea that the Constitution protects life from the moment of conception is simply you projecting your own ideas into it.
1. "The first fallacy of your argument is that those who wrote the Constitution were modern conservatives."
The first problem in your post is a failure to understand that the classical liberal is the earlier term....today they would be known as conservatives.
Conservative philosophy is based on individualism, free markets, and limited constitutional government.
This defines the Founders.
2. "...therefore the government cannot restrict abortion in any way because they are not mandated by the Constitution to deal with this issue. The government has no right to impede, restrict, or hinder a woman's right to determine what happens to her own body."
You are very close to being correct in the above.
It was an erroneous decision by the Supreme Court to decide based on an imaginary right.
But...had you said that the states can decide the issue of abortion, I would agree.
3. " ...nothing in the Constitution recognizes that life begins at conception."
But the Constitution has no purview as to when life begins.
Unfortunate that you don't realize that.
So, it seems that between the two of us, the failures are yours.
Don't you agree?