How can one combine reverence and contemplation of the meanings of Al-Fatiha and the praises (Tasbihat) in prayer with keeping track of the number of its rak'ahs, in the event that focusing on one causes the other to be forgotten?

There is no contradiction between having khushu' (devotion/humility) and keeping track of the number of rak'ahs (units of prayer); rather, khushu' is more conducive to keeping track. Not keeping track is from Satan, who confuses the worshipper during their prayer so they do not know how many rak'ahs they have prayed. The cause of forgetfulness is the whispers of Satan, not contemplating the recitation or having khushu'. It is recommended to strive in supplicating to Allah to inspire the worshipper to combine khushu' with keeping track of the number of rak'ahs and to keep satanic whispers away from them.