Josh - I'm sure some will critique your descriptions, but they are fairly accurate IMHO.
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.