I stand corrected...I think. I should have provide the following reference along with 4-41-1:

4-41-2: A try for goal is an attempt by a player to score two or three points...

It seems that 4-20-1 doesn't comply with the definition of a try as per 4-41-2.

Should we accept the free throw as a 1 point try per 4-20-1, then it would reason that the penalty would be 1 free throw, since being fouled in the act of shooting results in two free throws for a two point try, and three free throws for a three point try. In each case, if the try is successful, one free throw would be awarded.

This is all purely definitional. Keep that in mind.
There is an act of shooting as well as a try for goal during a FT. However, the penalty for such a foul does not involve awarding any FTs. Why? Because the rules only specify to award FTs for fouls committed against a player trying for a FIELD goal or when a team is in the bonus.
I agree with rules explanation provided above by BigCat.

I agree with others that a Ft shooter fouled in the act will be intentional. However, if for some reason an official declares that it is not intentional or flagrant i believe the only choice left is a common foul.

4-41-2 says a try for FIELD GOAL is attempt to score 2 or 3. Your quote of 4-41-2 left the "field" part out. A FT is a try for goal but not for a "field" goal. If you look at the defintion of common foul you will see that this example fits if you declare it wasnt an intentional or flagrant foul. There is no authority in the rules to give a FT shooter who is fouled in the act of shooting a FT for the foul unless they are in the bonus. (again, assuming it isnt intentional or flagrant) It is not in rule 10. This is another reason intentional or flagrant is the right call. I've seen over the years a player or two shoot a jump shot free throw near the elbow. Even in that location, closer to the top lane spot, a foul of the shooter in the act would likely still be intentional...

Doh! Again, I stand corrected.

Thanks for the discussion. Helps to sharpen the brain as we enter the season.