Faith without reason is blind. Blind faith isn’t true faith. God is the author of reason and logic therefore any faith in God must also be reasonable and logical.
When faced with the “testimony” and “burning in the bosom,” you have to break through that first. This is a good start.
I would also refer to St. Peter telling us to “always be ready to give a REASON for the hope that it is within you.” (1 Peter 3:15).
St. Peter tells us that REASON is important. You might also point out that the Greek word for Jesus as
the Word of God is “Logos,” which is the root of Logic, and Christians from the earliest times have spoken of the link.
Don’t let them weasel out by discounting the Bible “insofar as it is translated correctly;” we have tons of documents in the original languages (Greek, Hebrew), so we can see the un-translated originals. Even if they want to debate translation, they need to back it up from those source documents, not just use that phrase as a vague dismissal of anything they don’t like.
You might also ask what human faculties set us apart from the animals. Reason is clearly one of them, and clearly one of the things that makes us in the “image and likeness” of God. If God gave us the gift of Reason, it must be for something–and He must be eminently reasonable (He is Reason itself).
As others have also pointed out, everyone can claim a testimony. I can tell them honestly that I have a “burning in the bosom,” a solemn testimony confirmed numerous times, that the Catholic faith is absolutely true. Anyone of any faith can claim the same. And the Scriptures (Jeremiah 17:9) also say, “The heart is deceitful above all things, and beyond cure.” So are we just to brandish our subjective testimonies and ignore any objective measure?
Ask them to give that “reason for their hope.” Ask them how they know they are right in interpreting their feelings. Ask them if they could possibly be wrong about that interpretation–and how can they say that their interpretation is right but others’ interpretations of their own feelings are wrong. Ask them how they know their feelings are from God.
If they won’t budge anywhere, I would tell them that it is impossible to have any sort of reasonable conversation with them, warn them that passions and twisted interpretations can lead one to hell, and send them on their way, inviting them only to return when they are willing to have a reasonable discussion.
Also,
do NOT read any of their texts unless they will read something that you give them. Check up on them if you have future discussions; give them pop quizzes to “trust but verify.” Don’t let them get away with it. You won’t read their materials if they won’t read yours.