What does it mean to Write in the Spirit of Tolkien?

[Lalaith]

It seems that all the men who ended up marrying in LotR, did NOT, as a matter of fact, idealize the main woman in their lives.

Yes, you're right, I hadn't thought of that. Although I'm not sure we actually know whether or not Aragorn idealised Arwen before they married...
The other thing I was thinking about was the way that the idealised women in Tolkien behaved to the men idolising them. Even though they are - presumably - good and honourable women, they blithely accept the worship as their due, they don't have a problem with it. Compare this to the good and honourable Aragorn's shame at being worshipped by Eowyn.
And I also agree with you about this:

because righteousness is, well, passé (which is a real shame).

It is quite possible for good men to be interesting as well as bad ones. But to go back to Romantics, the trend of which you speak is linked to righteousness, in that it is about having and pursuing an ideal, and probably why I had to go back to the Victorians to come up with Romantic men (idealisers of women) created by female writers. I've come up with a couple of examples that you're welcome to knock down if you don't think they fit. (Particularly as I still need a better definition from you of what a Romantic man is! Is Gatsby one, for example? He's certainly not righteous...)

Anyway, what do you reckon about Adam Bede (George Eliot)? Also Tertius in Middlemarch...And I'm pretty sure Mrs Gaskell had a couple of similar types but I can't remember them right now... One thing though, these female-created idealists typically idealise the wrong women.