I think that your uneasiness at reading that sentence is in an apparent aspectual "clash". It is not really about tense or inflectional forms of the verb.
When you say:
it is understood that X will refer to a punctual event, an event that happens once at a discrete, identifiable time, e.g.,
since I stopped smoking...
(ever) since the chandelier broke...
(ever) since I won the tournament...
It sounds odd if the event in X has non-punctual semantics, referring to an event that takes place over a long stretch of time
?(ever) since I was living as a non-smoker
?(ever) since we were living in a lightless house
?(ever) since I was living the life of a tournament-winner
The verb know has both punctual and non-punctual senses. The punctual sense is equivalent to meet, and the non-punctual sense is equivalent to be acquainted with.
The oddness of the sentence will vanish if you interpret know punctually, i.e.,
The considerable debt of gratitude I have incurred to Mr X since I met him, has continued to grow during this last period.
If you translated the sentence from a language which has separate preterite and imperfective forms, there would be no such ambiguity in the original sentence, but English does not have such a distinction in verb forms.