Josh - I'm sure some will critique your descriptions, but they are fairly accurate In my humble opinion.
It's interesting that you mention church discipline for professed believers that prove to be imposters. We are facing one such issue right now in our church. There is more to it than just a repudiation of faith, but that is the crux of the problem. We are calling on this brother to repent. We pray that he does.
I am one of those Reformed Baptist's that hold to a "new" new covenant, not a refreshed covenant. And I agree with you. This thread should not be a debate between paedo's and credo's. That issue becomes beating a after awhile.
There are times when the unity between Presbyterian's and Baptist's seems tight. Then there are time when we seem so far apart that nothing will bind us together. Ultimately there is Christ, but He is often relegated as secondary to our debates. That is sad. I'm not impugning anyone by saying this, just stating a reality.
Our differences are real, I pray they are seen as secondary to the true faith we share in Christ.
"Alluding to passages such as Jeremiah 31 and Hebrews 8, the Reformed Baptist says in the New Covenant, all will know God, from the greatest to the least of them, whereas the Reformed Paedobaptist will see an “already/not yet” aspect to the aforementioned passages. "
Reformed Baptist, including myself and the Most Divine Sam Waldron would say that Reformed Baptist see an "already/not yet" aspects also..
We would say it has been Initiated and it progressive until it is fulfilled in consummation.
The "All will know me" aspect is not perfected until it is completed in consummation. But has already begun...