So close, but commits the fallacy of false dichotomy: this claims that either we accept elect infants and thus must baptize them /or/ we can only accept infants are elect by some other means of grace than is revealed in Scripture.
You are only proving my point that the new covenant is irrelevant to the question of baptism. However you construe the new covenant, the new covenant concerns the elect, and the elect includes infants. To remove infants from baptism, you have to separate baptism from the new covenant. That is the point.
Baptism is a "sacrament" and is defined as that which is a visible sign of an invisible grace, positively commanded by God, elements prescribed by God, and confer grace on believers and seal that promise in grace by the Holy Spirit. (Muller "sacramentum")
If you are going to accept this, you will have to also accept the Reformed view of baptism as a sign and seal of the covenant itself. This equates to saying that baptism is the means by which God seals the promise of His covenant to the elect, including elect infants. But I seriously doubt you will allow this. So you will need to explain how you propose to separate baptism from the covenant. At which point you will deny what you have affirmed from Muller. As with previous exchanges on this thread this challenge will likely be left unanswered.
Baptists define the Covenant of Grace as those who are truly sealed by the Spirit and therefore cannot be outside grace - false professors then excluded so it is not by profession of faith as we are continually maligned, but it is by possession of faith because the Spirit cannot fail those whom He seals.
Are elect infants sealed by the Spirit? You can use whatever turn of phrase you please, it is not going to remove elect infants from the covenant of grace.
Answer: the faith we have in our God, Judge of the earth and all those who walk thereon, who will always do what is right.
God has given means by which He signifies and seals His promises. God has provided baptism. One should hang his faith on what God gives.
But through that earlier handwringing in this thread, you then see that the paedobaptist likewise "inherently thinks in terms of baptism being something an individual does" as well.
How could we baptise an infant who cannot do anything and then think of baptism as something the infant must do? Infant baptism is a very clear testimony that regeneration is monergistic. Anabaptism did not hold to monergism. That is why infants were excluded in the first place. It was something the individual must do. That practice of baptism reflected the theology. I will say it again, I am thankful my "Baptist" brethren have become Reformed when it comes to soteriology, but when it comes to baptism they are not Reformed. Their doctrine of baptism is synergistic.
Baptism IS something done physically - by and upon - people; yet is only efficacious spiritually by God the Holy Spirit .
If this were genuinely accepted there would be no reason to remove infants, since the Holy Spirit does this on elect infants.