My sense is that he was trying to understand modern life as a classicist would understand ancient times. Trying to create that heighten state of fragmentary deep meaning, etc. -- but mapped to the disillusionment he felt in the present.
Normally a classicist is involved in the function of:
Classicist -> immerses in ancient literature
Eliot's 'trick' is that he would attempt higher order functions and map the whole technique to the present:
[Classicist -> immerses in ancient literature] -> immerses a Classical understanding of the present,
which makes the present seem Classical in importance. Nor is that the only way to go. But I think one of the greatest things that Eliot offers through his poetry is this challenge to become more sharply critical (the same way philologists must rise to the level of their material, after translating, etc.). Hypertextuality helps a lot. But, as I think Tycho sort of hints at here and in other comments, the goal is to engage the whole approach.