Update: after the honeymoon phase with the biggsfix I still noticed unpleasant instability. Less than before, but too much for my own comfort. Especially unpredictability was annoying. Never knowing when it went sharp or flat. I let the Starla be and bought a nice McC that gobbled up my play time.
However last sunday I used the Starla in church, even though the instability was a risk and uncomfortable, but the guitar fit the set like a glove. Short story; sounded phenomenal, was a pain to manage. Me being me I got ispired to fix it. A quest was found and barked upon.
Short story/Sergio version: FIXED IT.
Lazlo version below (and I would read it if you own a bigsby).
I got a brainwave during the service: it occured to me that the bigsby itself might be the issue. It was stiff, not just because the spring was stiff, but because there is a lot of friction in the bridge itself, causing the guitar no to return to pitch. I noticed this friction last time changing strings, but did not think it through. I searched on the webs and youtube how to lubricate my bigsby (and took care to formulatw that search precise) And found this youtube vid.
It told me two things: I was right about the friction being the issue and gave me two paths to explore; lubrication and installation.
As it turned out: both were an issue. The bridge needed alignment and the bridge was lubricated, but with too much grease: it got sticky. Removed a bit of the grease and now the bigsby arm "falls" like the video above and the guitar became actually stable.
Abused the bigsby, and returned to pitch within 7 cents. Tuned it, repeated ithe test multiple times; same results. Let it rest over night: still the same results. I think I fixed my Starla!! Might be worth exploring for other Starla owners as well!