Tartil is a word which is very wide in meaning and significance. It may mean in proper order. It may mean with no haste. Pausing where you should pause and considering and giving it a proper order. And it may mean other things. I mean Tartil is a very interesting word with quite wide meanings to it. Normally it is understood by Tartil that without haste you should continue to recite the Holy Quran in the order fixed by Allah. Now there are two orders attributed to the Holy Quran. One is order of revelation and one is the order which was later on described to Huzoor-e-Akram and the verses were reorganized in that order.
So to us the second is applicable. At the time of revelation the first part was applicable. That as things are revealed to you, you say them, repeat the recitation of the Holy Quran with Tartil in the same order with proper attention and a good voice. All these things according to my comprehension of the word are included in this.
So for you it is that you consider the Holy Quran, the meanings of the Holy Quran. When you recite that means the attention is drawn to the underlying meanings as well. Consider or ponder over the meanings of the Holy Quran in the order in which Huzoor-e-Akram was directed by Allah to reorganize the Holy Quran’s verses. And then you will strike gold of unlimited meanings and philosophy underneath.