Alright, this last monday I was there on another visit, and I would say that I made some serious progress that time.
One rather odd thing that helped out a lot was actually that I had stayed awake all night the night before that day, so I was in that funny sleep-deprived state where I felt generally giggly and laidback, and I always smiled for myself a bit.
And even though I certainly don't advocate sleep deprivation, it was nonetheless a very helpful boost, and it made me capable of starting casual conversations with the people there and I felt much more at ease in general.
I also noticed that I got positive responses from this - everyone seemed more relaxed around me, and I had a chat with several of them after we were done for the evening and walked with them for a while and talked.
It was an extremely liberating feeling, and best of all, it seems to have worn off on me, since I felt very similar after I had slept a lot.

There was also that issue with the people who were instantly intimidated by me from the beginning since I appeared very insecure then, and that are having problems getting used to me when I am more confident;
one cool psychological trick that I have started using when I run into them is that I "swap roles", and pretend that they are the ones who are shy and insecure around me.
I find this very empowering, because it encourages me to put them at ease and show them that I am a kind and approachable person, and that situation is much easier to handle than the scenario when I thought of myself as the shy and insecure type.

I will continue working on this, I feel that it has been quite a milestone for me.
It was probably at least 15-16 years ago since I genuinely felt that way around new people, so it's about time, lol.