There are a few ways to thicken or weaken the atmosphere of the moon. One way would be to use a chemical reaction to create gases that would increase the thickness of the atmosphere. Another way would be to use solar radiation to break down the molecules in the atmosphere, thus making it less dense.
The most dense atmosphere area of the moon is not the cause of max high tides. The most dense atmosphere area of the moon is the cause of the Moon's gravitational pull. The less dense atmosphere area of the moon causes most damage.
This is a difficult question to answer without more information. Based on the information given, it seems likely that the less dense atmosphere would mean that there is less gravitational pull at that area of atmosphere from the moon's land. This would mean that less gases are present, and therefore the atmosphere would be less visible.
Moon atmosphere can also be thickened by placing a moon-like small disc shaped moon for the moon (in space and near to to the moon). This disc shaped device can suck in or absorb gases from space and throw within the gravitational pull of moon for gases.
But for deciding on that we need this information-
1. Is radiation emission more in thick atmospheric area of moon or
2. Is radiation emission more in thin atmospheric area of moon?
The two are not related.
I think a thick atmosphere will protect the moon and Stop our plans to destroy the moon to get rid of high tides.
Thick atmosphere might not let our plan meet success.