I like the first. The quickest way to make SF seem quaint is to place it in time, especially in the near future. Keep the date references vague and you guarantee immortality!
You might also do a combination of the two (good name for a song). Choose a year zero, but don't tell the reader what it is. Strictly a reference point for you. Then you can say X years ago. You can even say things like, in my father's day or grandmother's day, or when I was a child. And if the reader thinks she has it pinned down to the 2020s or whatever, then good on her. Only you know the true secret!
I'd think about doing two things. First start with the Mad Max approach - no dates, just an event that everyone sort of agrees upon as a starting point eg the oil wars. Then go from there forward using not years but lifespans. Eg grandma says - "when I was a little girl before the oil wars ... " In that way you get a sort of rough estimate of time.
The second thing you can do is date things through language. Simak used to do it through his countryfied terms which sort of shifted your feel as a reader of when things are happening. But for you you might want to use more cyberpunk terminology (assuming that's the future you're planning on). Think the expanse and its slang.
I think what I'm going to do with this is as follows, part of it being that I had planned using the year as a series order designator (iow; 2028, 2029, 2030, etc..)
There are a few red-letter events in the pre-history. Many of those however span long periods of time, except two. The first would be "the Black," which is the day that America's infrastructure collapses. That I don't think works in that there would naturally be chaos after for some time.
The second is "the Gathering," which is initiated (though takes months) by the President/Mad Clown via his final mass communication to the people. "Get to the Bos-Wash megaregion now, or be cut off."
I think I'll use the Gathering, more specifically that communique, as the "zero date" for a few reasons. First, the Mad Clown's vanity. That will be the date that he determines is the start of
'his' new America, Consolidated America Sanctuary East or Case City. In his mind, that's day one, year zero, the day the nation is his absolutely. So, naturally all time starts then, to him.
Blah, blah, blah, there are other reasons that justifies that being left alone, until quickly he's gone, and the 'Restored Constitution Federal Government' takes power. To simply keep things moving, they initially stick with his policies (another reason) and then come up with a policy of their own called "the Policy of Erasure." The point of the PoE is to get the people to comply and forget the past. So, it fits they'd be happy to have reset dates as well (still another reason).
To that end, that date roughly 2020 I'll make G+0. Anything before will only be remembered or documented by G-4 as an example. Anything subsequent, like what is currently 2028 would be G8 (G+8). In rare cases when specific 'years' are noted (except for the RCFG everyone has lost their regard of dates), I'll use that system. I'll then apply that to the novel title / series title - date.
Ex.:
The Abolitionist
L... S... G8
Lest ye be Judged
L... S... G9
The Violence of Lambs
L... S... G10
Thanks for the help folks, I think that works nicely!
K2