Is it obligatory to change mosques for fear of falling into ostentation due to the glances of fellow worshippers, and what about accusations of abandoning congregational prayers?

One should disregard the whispers of showing off (riya') and continue praying in the neighborhood mosque, unless there is another legitimate intention, such as increasing one's steps. Abandoning a good deed for the sake of people is showing off (riya'), and performing a good deed for the sake of people is polytheism (shirk (definition)), and sincerity (ikhlas (definition)) is for Allah to protect you from both. Riya' is a matter of the heart, so as long as a person's intention in worship is to draw closer to Allah and seek His pleasure, then he is sincere.