In the normal days there are a lot of people in the Holy mosque of Makah and this is a common trend there. If you perceive that someday this crowed will go back and you will have the whole place free then you are hoping for nothing. This is the only place in the world where people come and perform prayers in the hot summer of June and July no matter that this is a dry and hot desert of the Persian Gulf. This is not possible for you to perform Umrah in that time when there is nobody else there except you, but it can be possible that you can perform the Umrah when there is less number of people around you and you do not have to face a huge rush there as well.
In this situation you have an advantage that you can perform all of your prayers and practice peacefully without any tension. Mostly a number of people have to face a great difficulty at the point o Hajr-e-Aswad and in that time due to less number of people you can easily get a chance to go there.
