Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Al-Shatibi (may Allah have mercy on him) stated the definition of Bid’ah (innovation), the text of which is as follows:
'Among this Bid’ah is to adhere to given manners, modes, ways or aspects at a definite time, which have not been set by the Shariah as such.'
Based on the above definition, what you have mentioned as a gathering to read the Qur'an at those times is a Bid’ah which is forbidden by The Law Maker. The matter is more breaching of Shariah rules if the recitation is loud disturbing the people who pray. However, by going to Friday Jumu’a late you are missing a lot of good.
It is reported in Saheeh Bukhari and Muslim that Abu Hurairah (Radiya Allahu Anhu) narrated that the Prophet (Sallallahu Alaihi wa Sallam) said: “Whoever makes Ghusl on Friday (like purifying oneself from Janabah) then goes (to the Mosque), it is as if he gave a camel as a Sadaqah. And whoever goes at the second hour, it is as if he has given a cow (as Sadaqah). Whoever goes at the third hour, it is as if he has given a horned sheep, and whoever goes at the fourth hour, it is as if he has given a chicken. And whoever goes at the fifth hour, it is as if he has given an egg, ….”
So it will be more correct for you not to delay going to the mosque so that you do not lose a lot of benefit. But you try to change the innovation and noise that are taking place with wisdom, good admonition, and debating with best manners and soft words.
Allah knows best.