Your quote from the Congressional Globe hurts your argument. It shows that the Congress didn’t presume common law would automatically be in effect. By your own admission, the English statute was passed nearly 100 years prior ... which means it would be part of the common law. This shows there was selectivity about what parts of English common law were respected in the new United States.
Sheesh - of course Congress didn't presume common law would always be in effect in all things - they were quite specific in some areas - outlawing bills of attainder, for example. So yes, there was selectivity, but many terms in the Constitution are taken directly from common law. "Natural born" is one of them. Again I remind you of President Reagan's attorney general writing that we follow jus soli..
In case you don't realize this, some colonies were established and had laws/charters dating from before the 1708 English statute making those born of English citizens abroad natural born.