Another 'sounds like you're doing fine, try not to worry' from me.
Also to echo the pp who said that different year groups (of parents and children) have different dynamics and don't worry too much.
I was keen for school gate friends. (I always feel a little bit awful when I read the 'I have enough friends, why would I want to get to know any mums' stuff on here.) We hadn't lived in the area all that long and I'd found it hard to make friends with three toddlers to supervise, so I was very open to the idea of new friendships.
First class, the cohort of parents was never unfriendly, and there weren't any cliques really, but just wasn't very active/sociable. We had a lot of fun organising their Y6 leavers party actually, but that was the exception.
Second class, much more friendly and proactive group of parents, very keen to build relationships with each other. I still see seven or eight of them regularly (and only one from the first class) now the kids have moved on to secondary school.
I think all of my children (two in the second class) had similar experiences in terms of parties/playdates etc. I can only think of one occasion throughout the whole of primary where one of the kids clearly benefited from my friendship with one of the mums. It really does sound to me like you are doing enough and, while I don't think it doesn't matter at all, it doesn't matter as much as you think.