Hi
I have just dabbled a little with tubes, far from an expert.
But, all the output transformers I see are either push-pull or single ended, so I think your friend is right. I would not use a transformer designed for SE in a PP application.
I'm not sure if it's impedance or power. PP tranny's have to support more output power then SE.
Magnequest is supposed to make good iron
http://magnequest.com/products.htmIn the who makes the best iron posts, I normally see them get at least one mention
Depends on your budget, Magnequest is pricey, Hammond tx's are more affordable. There are many others like Lundahl, James, Tamura.
Good luck with your project.
Randy