Is it permissible to lengthen the distance to the mosque on foot on Friday with the intention of attaining the virtue of walking mentioned in the Hadith: "He walked and did not ride... for every step he took from his house to the mosque, he would have the reward of a year's worth of fasting and praying"?

There is no evidence preferring going to the mosque via the longer route. The fundamental principle is that a Muslim should not seek hardship in worship when an easier option exists. Hardship is not sought for its own sake; rather, one is rewarded for it if it accompanies an act of worship, as the Prophet, peace and blessings be upon him, said: "Indeed, your reward is commensurate with the extent of your toil." The best approach is to choose the easier option in all matters, as long as it does not involve sin. The easier the action, the better it is.