Did Jesus actually instruct rather than predict Peter to deny him three times so he could live on and found the church?

Yes, Jesus instructed rather than predicted.

The immediate objective for his instruction was the fulfillment of the words which he spoke, “Of all of those which you gave me, I have lost none.”

Jesus met that objective for the ten by his orchestration of the scattering.

The adverse reaction of Peter to the instruction Jesus gave to scatter showed Jesus that Peter would fail to follow his orchestration of the scattering.

Peter’s inability to deny himself and follow the instruction of Jesus to scatter put him at high risk for becoming “lost”.

Peter needed another opportunity to “get behind" Jesus. The three denials were that opportunity.

Jesus prayed that Peter would have faith to follow him, and, at last, Peter did follow him when he denied him three times.

So, Peter did live on.

But Jesus never had as an objective that Peter “found the church.”

I say these things only in my own name.