I can't imagine Corbucci had a (loose) trilogy in mind
If you only consider the working titles for the film he wanted to make in '69, Lo Specialista a mano armata and Il Ritorno del Mercenario, then he clearly had a Zapata western in mind, about a warfare specialist, to be played by lee van Cleef. I don't know why the idea was dropped (nobody seems to have a clear answer to that), but he suddenly decided to do a film with Halliday. It was a co-production with France and Germany, but his Italian producer agreed with the plan to do this film (so to give up the other one), probably because the expections were high: Halliday was a big name in France, Corbucci in Italy and Adorf in Germany.
On the other hand, the French wanted to shoot the film in Tunesia or Morocco, but Corbucci absolutely wanted to work near Cortina d'Ampezzo, were he had already shot The Great Silence. To him Gli Specialisti was a 'cold' western. Look at the fur coat Adorf is wearing (and look how he is sweating before he is shot by Halliday in the finale - that scene was shot in Rome, where it was scorching!). Halliday preferred to work in Northern Italy too, because he had a villa in the neighbourhood. Ironically Halliday stayed with the group most of the time, but Françoise Fabian spent some time in his villa after she had accused the Italian extras of sexual harassment and threatened to leave the project.
There are some similarities between Django and Silence (the crushed hands symbolism for example, you can read about it in my reviews of both movies), but I don't think there's a real connection, they're fundamentally different movies. There are also some similarities between (the characters) Silence and Hud, both are loners, both are intovert, tragic characters, but Silence is still some kind of idealist who helps the poor against the rich, Hud is a cynical misanthrope, who has no friends and no ideals at all.