Correct vs. incorrect is a very prescriptive frame to consider this matter in. While following sets of rules is a great way model nearly universal usage patterns (e.g. breaking the subject-verb-object model is so unused that 'wrong' is an accurate descriptor for an error such as 'Store go I'), preposition usage tends to follow relatively nebulous rules (guidelines?) and changes relatively often. Patterns of usage are harder to distill down into actionable rules. We still have some usage 'rules' ('with the morning's would clearly be so rarely used that we could consider it wrong); however, what sounds right or wrong to you can often be quite reflective of the state of English that you grew up with.
For instance, the advertising slogan "Like a good neighbor, State Farm is there" apparently drew the ire of many English teachers at the time of its launch (who preferred 'As a good neighbor...'). Yet I suspect most people today would hear 'like' as perfect reasonable, and may even hear 'as' as dated. 
With that disclaimer out of the way, the sentence parses meaningfully for me, although as a matter of style, I would prefer the order of prepositional phrases be reversed, as this would structure the restrictions of time in order of granularity (in contrast, the current version seems haphazard):
on September 27, 2017 during the afternoon and on September 28, 2017 during the morning
Or, replacing 'on' (which limits time scope) with 'of' which refers to a property of the previous noun, as you suggest, would allow for a more elegant expression of the same concept. With that said, a quick email to colleagues isn't really a context that merits deep thought about minor style quibbles.
Bottom line: this is more a matter of style and trends in acceptable usage than errors in prescriptive grammar. You might check your favorite style guide if you're still looking for a prescriptive solution.