Does attempting to pray and perform ablution in front of people—in order to overcome the intrusive thoughts that might dominate when one is alone—count as showing off and seeking a reputation?

It appears that what the questioner is doing is not hypocrisy (riya'), as long as he does not intend it to be so, especially since he finds in it a cure for his whisperings (waswas). He should rely on Allah, turn to Him, recite the Two Protectors (Al-Mu'awwidhatayn) frequently, and disregard these whisperings. If he doubts his ablution or prayer, he should not pay attention to those thoughts, because excessive doubt leads to a kind of obstinacy.