I've addressed it on numerous occasions and will do so again here.
The moral answer to the situation is to let the fertilized eggs burn. However, that doesn't mean the fertilized eggs weren't human beings. It means that in a situation demanding someone die, the fertilized eggs are the best candidate because they feel no pain, aren't self-aware, etc. But we only create these distinctions because we are forced to kill someone in your scenario. And that's not analogous to an abortion, where no one has to die.
Yes, the entire point is to make you make a choice. In this case you think it is preferable to let 1,000 embryos die as opposed to one baby. My guess is that would hold true regardless of the number of embryos. 10,000. 10 million. You, and basically every person on earth would likely allow more "people" to die than Hitler killed in the Holocaust in order to save one baby.
That tells you, inescapably, that you do not view both entities as equally deserving of protection and equally deserving of life. If you did, you wouldn't allow 1,000 people to die to save one.
As for whether it's analogous to abortion, the thought experiment isn't about abortion, it's about how absurd the idea is that life begins at conception. Clearly life at conception is not worth even 1/1,000th that of life outside the womb, so let's stop pretending we should treat them the same.
Question: What would it mean if I decided to save the fertilized embryos and leave the 1 day old baby to die? Would it meant that I didn't really believe the 1 day old baby was a human being? No. It would mean that I came up with some rationale that placed the value of 1000 embryos higher than the baby. Whether you would consider that moral or not is irrelevant: I didn't choose one over the other because I thought one was a human being and the other wasn't.
It would imply that you thought saving the 'lives' of 1,000 embryos was more valuable than of one baby. The conclusion there isn't nearly as stark as the other way around because then you would have to do some more digging to find out what that relative valuation was.
Literally the only way that the argument that life begins at conception and is entitled to all the rights that we have as full people is an accurate description of someone's true preference is if you saw a baby right next to a single embryo and said you were equally likely to save both. Literally nobody actually thinks that way, because that's fucking crazy. Hence, we should stop with the 'they have full rights as people at conception' nonsense.