I would say if there's no reasons to ttc now, maybe his mates are saying when you have a baby you can kiss goodbye to nights out and doing things when you want. Pretty much common sense, but maybe he's scared how it will impact your lives, so wants to wait a bit longer.
I agree the genetic counselling is better done anytime before TTC, but I'm sure you've reassured him he has a good life with the problems, that's what really matters.
In a way we don't know your financial situation, but he could be thinking in terms of Brexit, what impact will that have on money etc. He could be worrying about work.
Just because figures show it's feasible now, he may be reluctant thinking I don't want to get in over our heads. I don't know if that makes sense.
But you have one issue really, which is if you move, you have a baby, go on maternity, will you still be able to live comfortably. That could be a reason to go for it whilst you're at this old house and money is easier, over having a bigger mortgage, more council tax.