Does this do want you want?

    Cases[Options[i, MetaInformation], 
     HoldPattern["ExposureTime" -> ___], Infinity]

or even simpler because it is `Rule`s all the way down:

    Cases[Options[i], HoldPattern["ExposureTime" -> ___], Infinity]
    

>     {"ExposureTime" -> 1/65}

All-in-one:

    With[{wanted = "ExposureTime"}, 
      wanted /. Cases[Options[i], HoldPattern[wanted -> ___], Infinity]] //
      N