The Sunnah of the Muslims Is to Pray at Any Time in Front of the Kabah

The tawaf is a continuous ritual that has gone on non-stop for 14 centuries except in limited times of crises where things happen in front of the kabah. The sunnah of the muslims has been to have janaaz al-salah at any time whenever the janaazah is ready even if it is after fajir or after Asir. It was not a problem.