You are hugely, massively unreasonable!
No, all 15 of you don't have to go there! If he decides to host you, then it's you (and maybe his father and possibly siblings who live with you two, check first!) who he's decided to host, not everyone else. If he wants to host them he'll invite them. You all don't have to go everywhere as a giant posse.
What's all this about he chose the family takeaway night over the Sunday dinner option? See it for what it truly was - he chose the lesser of two evils. He didn't want to go to either.
He's chosen to move 50 mins away. He made that decision as an adult. A 50 min drive after work, plus whatever time he spends at your place, will leave him home late on a Friday and knackered on the Saturday. If he has chores or childcare to do on a weekend (not unreasonable) then he'll feel like he hasn't even had a weekend off at all. For that to happen 25% of the time would really, really suck. I suspect he's moved so far away for good reason, he wants to break this family dynamic of meeting up so frequently and with everyone. He's moved far enough away that he's not going to be having people knocking on his door to pressure him into attending.
His girlfriend who he lives with is his primary family now OP, you and everyone else are secondary. That's how it should be. It's no good blaming the GF for this situation with visiting - he chose her! He's happy with her values, he probably shares them.
Visiting for special occasions is plenty. Especially as it sounds like there will be lots with such s big family, which is why he's made a point of telling you it's only going to be if he really wants to and not to expect it. If several people have birthdays in one month, for example, you can expect him not to be at some of them.
He's literally told you that's how it's going to be. That's not an opportunity for you to negotiate with him for a once a month visit or to try to pressure him into hosting everyone. Accept his decision gracefully, without arguing or sniping at his GF or sulking. He has every right to make his own decisions. You need to let go. Why he's decided to do this is irrelevant. If he's taken his GF opinion into account that's great, it's what he should be doing as her partner. The pair of them have made a decision they are happy with, that's what adult life with a partner should be like.
"We have strong family values" is sounding a lot like "I always get my own way when it comes to family".