Wow that is in-depth analysis - thank you! You obviously have a lot of background in the Greek so I look forward to hearing more.
My comment is much more superficial but I still want to indicate my agreement - I think you are right and that it is inherently Epicurean to live passionately - to realize that time is of the essence because life is so short. So as you say we just don't "stroll around" (unless at that moment it is the most pleasurable option to us) we eagerly embrace life and the opportunities for pleasure it gives us. We should try not to waste a moment - and the words PURSUE and FLEE do communicate more strongly the energy we should invest in our living our lives.
Now no doubt some will wonder if "fleeing" doesn't indicate anxiety and fear, and I would say that would probably be a connotation of the word to limit in this context, but to the extent both pursuing and fleeing indicate "urgency" and "seriously" and the like, I think those completely apply.