That wasn't precisely the question being asked. Is it not true that baptism is an administration of a promise? Isn't that what a covenant basically is, a promise? If not, then why is Acts 2:39 (this promise is for you and your children)? Also, Gen 17, which is often used to support paedobaptism makes reference to God's promise to be the God of Abraham and his descendants.
If baptism is a sign and seal of covenant, then I take this to mean that it signifies a promise. However, if the sign does not necessarily apply to the one being baptized, then it is simply a general statement or picture of the gospel, without reference to the status of the person receiving the sign. Is this right?
I agree with the rest of what you said about safeguarding against baptismal regeneration and all that stuff.
Here is how scripture deals with this very question in regards to Israel. As Christians we are God's people. Instead of circumcision we have baptism. Instead of being just ethnic, we come from all over the world. But it is the same fundamental. The Church is God's people.
Romans 9:4-23 KJV
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4] Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;
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5] Whose are the fathers, and of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen.
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6] Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
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7] Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.
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8] That is, They which are the children of the flesh, these are not the children of God: but the children of the promise are counted for the seed.
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9] For this is the word of promise, At this time will I come, and Sara shall have a son.
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10] And not only this; but when Rebecca also had conceived by one, even by our father Isaac;
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11] (For the children being not yet born, neither having done any good or evil, that the purpose of God according to election might stand, not of works, but of him that calleth)
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12] It was said unto her, The elder shall serve the younger.
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13] As it is written, Jacob have I loved, but Esau have I hated.
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14] What shall we say then? Is there unrighteousness with God? God forbid.
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15] For he saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
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16] So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
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17] For the scripture saith unto Pharaoh, Even for this same purpose have I raised thee up, that I might shew my power in thee, and that my name might be declared throughout all the earth.
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18] Therefore hath he mercy on whom he will have mercy, and whom he will he hardeneth.
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19] Thou wilt say then unto me, Why doth he yet find fault? For who hath resisted his will?
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20] Nay but, O man, who art thou that repliest against God? Shall the thing formed say to him that formed it, Why hast thou made me thus?
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21] Hath not the potter power over the clay, of the same lump to make one vessel unto honour, and another unto dishonour?
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22] What if God, willing to shew his wrath, and to make his power known, endured with much longsuffering the vessels of wrath fitted to destruction:
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23] And that he might make known the riches of his glory on the vessels of mercy, which he had afore prepared unto glory,
There are instances in scripture where those thought to be saved were not saved.
Matthew 7:11-27 KJV
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11] If ye then, being evil, know how to give good gifts unto your children, how much more shall your Father which is in heaven give good things to them that ask him?
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12] Therefore all things whatsoever ye would that men should do to you, do ye even so to them: for this is the law and the prophets.
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13] Enter ye in at the strait gate: for wide is the gate, and broad is the way, that leadeth to destruction, and many there be which go in thereat:
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14] Because strait is the gate, and narrow is the way, which leadeth unto life, and few there be that find it.
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15] Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves.
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16] Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?
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17] Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
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18] A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.
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19] Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
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20] Wherefore by their fruits ye shall know them.
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21] Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven.
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22] Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
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23] And then will I profess unto them, I never knew you: depart from me, ye that work iniquity.
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24] Therefore whosoever heareth these sayings of mine, and doeth them, I will liken him unto a wise man, which built his house upon a rock:
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25] And the rain descended, and the floods came, and the winds blew, and beat upon that house; and it fell not: for it was founded upon a rock.
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26] And every one that heareth these sayings of mine, and doeth them not, shall be likened unto a foolish man, which built his house upon the sand:
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27] And the rain descended, and the floods came, and the winds blew, and beat upon that house; and it fell: and great was the fall of it.
If a covenant is ever broken it is not God who breaks it but the one who works iniquity. The one who never really knew the Lord because his heart was evil and at enmity with God.
I would be interested to see what all of the pastors and theologians at the Puritan Board would write to you in regards to your question. Perhaps you should ask them as well?
