What you named "Swing time option 2" is the standard notation of swinged eight notes and triplets used in jazz scores. See e.g. this example of Dizzy Gillispie's Night in Tunisia:
Note that the word "swing" is not even written in the score, as it is left to the musician's taste whether and how deeply swing the eight notes.
Edit: It was pointed out in the comments that Night in Tunisia was composed in straight feel, and while some notable musicians performed it in swing feel, I tried to add some less controversial examples.
Charlie Parkers's Donna Lee:
The triplets are played as triplets, the eight-notes are swinged.
Sixteen notes appear rarely in lead sheets, more often in solo transcriptions, but I found this example of Armageddon by Wayne Shorter:
Sixteen notes are meant to be played straight, and groups including sixteen notes as well, so here at the beginning we have a sixteen-note triplet, followed by two sixteen-notes, followed by 4 sixteen-notes, followed by swinged rhythm in the next measure.
However in this example from Charlie Parker's Billie's Bounce:
The group is meant to be swinged, i.e. the sixteen-note triplet should take time of the first swinged eight note. The resulting rhythm might not be easy to notate explicitly but at high tempo of the tune the swing will be rather shallow and the whole sequence can be played as an ornament, following intuition.
And for completeness All of Me by Gerald Marks and Seymour Simons:
Quarter-note triples are to be performed as written.
I'd like to point out that rhythm in various jazz performances often vary significantly, and is modified by the musicians. The widely circulated scores in turn are often not written not by composers, but transcribed from some particular recordings. Therefore one can certainly find performances which don't match examples I provided, and also different versions of the scores.