“Peter and Adam are dead, thus continuity!”
No, Peter and successors - thus continuity.
“Really, that’s ridiculous — but it’s your assertion: that the church is founded on a man who is dead.”
No, it is a fact that Christ founded the Church on Peter - and many Protestant exegetes agree.
“My assertion is that it is founded on the Jesus, God in human flesh, who died to pay for my sins and now lives.”
Jesus says Peter. I believe Him. You don’t.
“Which do you think would be the recipe for a living church?”
Whatever Jesus says.
“To be founded on a dead man who could not save himself, or to be founded on the Living God who saved many?”
To be founded however God said it was going to be. He said Peter. Peter it is.
“By definition, it does: Apostolic succession is the method whereby the ministry of the Christian Church is held to be derived from the apostles by a continuous succession, which has usually been associated with a claim that the succession is through a series of bishops.”
Continuous succession - you said those words. That’s the point.
“If they were not different they could not be successors.”
If there was no continuity there were no successors. You lost this debate already. Your own language has defeated you.
No, actually it hasn't; it has only shown you to alter meanings: first you said that the church was founded on Peter [and no-one else], and now you say Peter and his successors.