I think the situation you are describing is much more science fiction then you perhaps realize (and bad science fiction at that). It is not just a question of technology, but frankly it is a question of money. I know that I must come off as the worst kind of monster to talk of money when we are talking about human life, but it is a reality that must be acknowledged. Do some research and see how much money, time and effort goes into taking care of children who are born very premature. And see how often these children still die despite all the effort. So I feel the need to point out that your hypothetical question is not reasonable.
However, that being said, if I can imagine this fantasy sci-fi idea, my position would only change under the following circumstances.
1. The procedure of this "transfer" can be showed to pose less risk to the mother than a proper abortion.
2. 100% effective and 100% risk free birth control is provided to everyone 100% free of charge.(100% effective and 100% risk free birth control does not currently exist, but this is a fantasy scenario)
3. There are no longer people living anywhere on this planet who lack sufficient food, access to clean water, free and adequate medical care, and free education. And there are no longer human rights violations anywhere on the planet. Until this is true the money would be better spent on these causes then your baby machine.
And then even if these fantastical conditions are met, I would still allow exceptions in the case of rape (which would probably not exist the utopia I describe, but I mention it anyway).
So If this is the scenario you propose, then yes. That would change my mind about abortion. But I think you will agree that this is not realistic.