OP, huge sympathy. DS was like this, and he was like it (sorry) until year 2 of primary! He just found the separation really hard.
I'm going to go against the grain and say upping the number of days p/w doesn't make a difference. It didn't for my DS.
The things that helped: not making a big deal, positively OR negatively - being kind but being matter of fact; making a quick exit; having a super super empathetic teacher to hand him over to, who acknowledges rather than belittles their feelings, says yeah it's tough, come and have a cuddle, and right, let's get the books out / drawing started etc.
In yr2 of primary, I would literally "hand over" my DS to his class teacher: I'd put his hand in hers, and then I'd leave. He found that physical handing over massively helpful. She was a brilliant and kind teacher with a massive heart: that's what you need to find for your little one. They need to go from one person (you) to another person.
(DS's teacher also made me feel like there was nothing 'wrong' with my DS, whereas plenty of people DID make me feel that there was, including the eye-rolly parents of bullet-proof extroverts who'd barrel into class without so much as a backward glance.)
Turns out, years later, DS is highly sensitive and also super clever, and I think this has great benefits but also a lot of downsides. He's clever enough that "jollying" him along has never, ever worked, but he's sensitive enough that someone acknowledging how he feels and giving him a mechanism to live with those difficult feelings can do the job. He also appreciates calm, matter of fact-ness about things he finds difficult. "Yes, it's shit, but it is what it is, and this is what we'll do now," works for him far better than anything else I can do.
It's when people try to jolly him along / discount how he feels that he struggles - teaching him that it's OK to find things hard, but that he can come out the other side if he just sits with those feelings, is the most valuable lesson.
We do tend to live in a world that's not that great for sensitive souls, but they can find a way through, as my DS has done / is doing. You sound like a great mum, btw.
Sorry for the very long post! It just took bloody years before I realised all of this!!