No, it is not a “false dichotomy” at all. It is a relevant question that SHOULD be answerable by those who imagined the whole concept of purgatory from the start. How many years have they had to develop it???
Look, I appreciate the dilemma faithful Catholics find themselves in when they try to step up and defend the various and sundry unscriptural doctrines developed over the ccenturies. Do you, can you, admit that on this subject particularly the magesterium dropped the ball and could have worked a little harder on the details rather than leaving it up to the individual to figure it out for themselves?
Paul makes it easy in his instructions to Timothy:
“But avoid foolish and old wives’ fables, and exercise yourself into godliness.” (1 Timothy 4:7 DR)
The answer is that the Good Thief had both faith, repentance, and good works, as the pericope illustrates.