My Question: Does the real presence of the Eucharist persist even after digestion to the point of being taken out of the body by defecation?
The simple answer to defecation is no? The Catechism of the Catholic Church does not view the Holy Eucharist as a simple material bread once it is consecrated.
The physical appearance remain bread but prayer of consecration turn it into a real presence body, blood, soul & divinity of our Lord Jesus Christ.
The change of the entire substance of the bread and wine into the body and blood of Christ is called Transubstantiation.
The Catholic Church teaches that the faithful believe the Real Presence thru faith.
The Holy Eucharist, Vatican II tells us, is "the source and summit of the Christian life" (Lumen gentium, no. 11; cf. Catechism of the Catholic Church, no. 1324). Since the Christian life is essentially a spiritual life, we might say as well that the Eucharist is the "source and summit of Christian spirituality" too.
At what point can we say "the Eucharist has done its job"
St.Athansius said "God became man, so that man shall become god."
The Church Father called this divinization or theosis.
The Eucharist has done its job when you reach theosis, As St.Paul exclaims it is no longer I who lives but Jesus.
CCC1331 Holy Communion, because by this sacrament we unite ourselves to Christ, who makes us sharers in his Body and Blood to form a single body.
The Holy Eucharist in Gospel of John in Chapter6 separates the true followers of Jesus Christ from the body of believers who left Jesus because of this hard teaching (John6:66)
Now, since Jesus Christ is the Logos/Incarnate Word, the question is?
what is the surest biblical way of achieving theosis/divinization?
As Christian, they receives the Word/Jesus thru reading & meditation of scriptures.
We Catholics receives the Word/Jesus in His real presence in the Holy Eucharist body,blood,soul & divinity as food to nourish directly our body & soul to form a Union/Oneness with the Life promised by Jesus.
"Jesus said to them, “Very truly I tell you, unless you eat the flesh of the Son of Man and drink his blood, you have no life in you."(John6:53)
Now, I will leave this to all readers which way would surely arrives a believers to experience and exclaims what St.Paul said in Galatians2:20
"I have been crucified with Christ; and it is no longer I who live, but Christ lives in me; and the life which I now live in the flesh I live by faith in the Son of God, who loved me and gave Himself up for me."