Ugh. I'm almost embarrassed to say I listened to both in their entirety.
I am curious to know---since if I recall correctly you have issues with 1 John 5:7---whether you think that passage was received by the church or not. Turretin says much the same thing about that passage as he did in the section you read from him.
Turretin is rather baffling on 1 John 5:7 as he claims "all the Greek copies have it". We also have citations from others in the 17th and early 18th centuries affirming much broader support in the manuscripts than we can observe today. So either they were clueless and misinformed, or there actually were more manuscripts available that had the Comma Johanneum at that time than we have today. I suspect there is some truth to both of these speculations.
Now to the question about Turretin citing it as a problem for demonstrating textual mutilation...keep in mind he said that while under the impression that it was "in all the Greek copies from the very times of the apostles". The concern of mutilation doesn’t follow if the manuscripts reveal this was a very late addition to the Greek text.
Mutilation was charged against the Greek and Hebrew texts based on the assumption that the state of the manuscripts that came down to us in history are corrupt. The Reformed Scholastics pointed to the broad support for supposed “corruptions” in the Traditional Text of the Eastern Church as proof the text was not corrupt.
As for whether I would say the Comma Johanneum was received by the church...it certainly was by the church of the Reformation (and historically by the Western church...but that's Latin, and I don't put a lot of weight in "restoring readings from the Latin") but ultimately we are looking for that which can be argued "in all ages". I find it difficult then to be dogmatic on it's authenticity, but as it is in the Received Text of the Reformation and presents no theological problem, I preach it after a brief mention of the problems.