You want my DH -sorry, not going to happen ha ha!
Seriously though, I think you're shutting too many doors with this 'screening' business. A very quick overview of DH and our relationship should show you what I mean.
We met when I was late 30s and he was early 40s. We met through an organisation which was set up for people who wanted to meet friends (men and women - if you went in looking for a man they'd run a mile!)
We began seeing each other then decided to marry. We both wanted children but knew time was against us. We luckily had our DH when I was 44 years old - he was 50.
He's not old fashioned in his views about women in general. He's got two very feisty sisters, both of whom have brought their kids up to see men/women as complete equals and they'd have knocked that on the head from a very young age! We bring DS up the same. DS saw me at home with him all the time but we've drummed into him that, if dad had wanted to be at home and I could/wanted to support that, that was perfectly fine as would both of us working full time outside the home. It's a personal preference up for discussion/negotiation rather than a male/female thing set in stone.
But what he is, is supportive and very caring. I gave up work to bring up DS when he was born, because I wanted to. DH earns good money, easily supporting all of us. I had my own flat before we met so we put equal deposit down on our house and it's jointly owned even though he pays the mortgage. DH paid all the bills but gave me an allowance each month that was mine. I did what I wanted with that - he hated the idea of me asking if I could buy shoes or get my hair cut. He thinks that's demeaning so money went into my account and I did what I wanted.
There was and still isn't any question of 'house clean and tidy every day, dinner on the table when I get home'. He understood from the start that my priority was our boy. The house gets cleaned, dinner gets cooked but it may not be completed when he got home (and before now he's done dinner and finished the hoovering as I've had a pig of a day with DS when he was a toddler. We've all had that 'time shot by' day). He'd come home from work, take over DS whilst I did dinner and was hands on. I bottle fed and at the weekend DH took over all the night feeds so I could have a lie in. He used to do the middle of the night feeds too as in his words 'I can sleep on the train, you need to be alert for DS. He's the priority, you need to sleep'. I didn't give DS a bath for the first three years of his life as DH loved that bonding (and yes, he did wipe down the bathroom after the splashing). I also got to go away for a night or two every three months or so - usually as trade shows for an interest I have came up. DH would have a 'boys weekend' with his son - usually pizza, swimming, film, hurtling around the park and some sort of outing before they met me at the station. Though he was 50 when DS was born, he's not a 'granddad' style older father - he makes our younger friends flag sometimes!
He does all the ironing - he was out of work two years or so ago and took it over as something to do. I was running (still am) a growing on line craft style shop then so any help was very welcome! He got a job last year but he's kept up the ironing. He works away usually during the week now and sees it as his way of taking one job off my plate.
So yes, he is 'old fashioned' in that there's a 'traditional' relationship. But he couldn't care less if I work full time or stay at home (I now work part time as DS has just hit his teens and needs me less). DH's view is he earns enough so it's my choice whether I am home (full time or part time) or work (full time or part time). He'd have expected (and would have got) the same if I'd have been the one to earn the high salary - but I didn't.
His role in the family is the foundation that supports me and DS - he quietly holds us both up and does a lot to make our lives easy. He will drop everything if we need help and we know that. He's not a saint - I could write equally about the things he doesn't always get right - but neither am I.
But you wouldn't have spotted that in your 'screenings' - he didn't even see 'SAHM' or 'you do the cleaning/I do something else' as a thing. He saw supporting someone he loved as a 'thing'. You could miss someone similar just because you've never given a relationship a chance.