Is it valid to perform the Dhuhr and Asr prayers as a جمع تقديم (combining them at the time of the earlier prayer) while traveling less than 100 km from one's original residence, then arrive before the Asr adhan?

Your action is correct, and you are not required to repeat the 'Asr prayer. This is the madhhab of the Malikis, Shafi'is, and Hanbalis. It was also said that you are required to repeat the 'Asr prayer, and this is one view among the Shafi'is and Hanbalis. However, the first opinion is the correct one, because combining prayers is a concession linked to the existence of travel, and you did combine while in a state of travel.