Pilgrim
Somehow I thought you would mention Baptists and I almost ignored it.
However, I am sure you know this already; but maybe others might benefit from me saying this.
When it comes the Paedo-Baptists and Credo-Baptists. An important difference between the Covenant Theology of the WCF & the 1689 LBCF; is while there is much agreement between the two Confessions.
Nevertheless, there is one difference that I find quite significant. Namely, that the WCF teaches the New Covenant is a new administration of the Old Covenant.
The 1689 LBCF sees the New Covenant as the “New Covenant”. Namely “The Covenant of Grace”.
This has some implications in how this is played out in a few areas.
Such as how the WCF views circumcision connected directly with baptism.
Whereas, the 1689 LBCF sees more separation between circumcision and baptism.

This could be fleshed out a little more; but that is not the purpose of why I am mentioning this.

I mention this, not to debate this matter. Which I am not interested in doing.
Rather, because it gives an important aspect in understanding the differences we have.

Tom