LX says on the new TravelClub website that miles are credited for all published fares on SWISS (the site is down again right now so I can't find a link). I therefore think that they'll have to credit you miles for the EZE run.

If TC Silver is worth it is entirely up to you and your travel profile. For me the biggest perk was lounge access, but if you mostly fly in C anyway that's no additional value. Apart from that, I had a few operational upgrades based on status which were of course great, but are not guaranteed.
The 20% more miles are ok, and the priority bag handling and special phone numbers don't make much of a difference to me.

RE the possible JFK run, I'm also looking into doing that one and shall start a new topic on it.

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airOli, the Swiss Air Line.