Having a heart beat doesn't lead to sentience in any way whatsoever. Sentience is in the mind, not the heart. Nor, for that matter, does having a fully formed life necessarily lead to sentience. We can all agree that plants are not sentient. We all pluck plants and don't think twice of it. We certainly don't consider it murder.
My argument does not live and die on the basis of sentience. I do think there is something to be said for sentience in fetuses (especially late in the pregnancy), but I find that when you think about it, you can show exceptions that show that the definition of personhood does not require sentience.
I also think talking about abortion like a woman gets pregnant and just decides to get the fetus out of her like it's the first thing she thinks about hugely misunderstands the matter. Abortion is emotionally taxing and a lot of women are traumatized for life after going through the procedure. There are a lot of support groups and such for women who have gone through abortions. Abortion is a last resort for women who absolutely need it. The women who abort the most are women who are incapable of raising a child, whether because they can't afford to, or due to other reasons. The point being is, do we really want to bring a child in this world who cannot be taken care of? What's the point of this "right to life" if this life is not given the other necessities of life we consider to be rights? What's so morally good about throwing children into a world of poverty, suffering, despair?
At the end of the day, being "pro-life" is an incredibly privileged position to take. It assumes that children will be taken care of when they're born, when in fact the exact opposite is true. The children who would've been aborted before existing are the ones who end up living the worst lives, lives of misery, of abuse, of suffering.
I think you're generalizing a little bit on when a woman resorts to abortion. While I'm sure many women would use it only as a last resort, I also think there are some women out there who just don't want to deal with a child no matter what and just want to dispose of it as quickly as possible. This is a risk you run in a society that provides easy access to abortions.
On the contrary, I think it is a little privileged for any woman who is pregnant to say that she has the right to determine whether her child's life would be worth living. She knows exactly how her child is going to feel about the life it is born into and it's completely up to her to deprive her child it's right to life on that basis.