Any way to claim the Iron Throne as R'hllor follower?

[Cassilda]

I my actual game I had my playing dynasty embracing the R'hllor faith, but that, even as the holder of three lord paramount titles, marriage with any claimant is not considered by them an option because of the faith of my character, heirs or other relatives. The only marriage option I have are with some vassal dynasties that I managed to convert, or various people of Essos religions.
I have tried to having my ruler "visit chamber" of some Targaryen princess, hoping that having them as lover will avoid that "is an infidel" problem, but I never managed to have that happen, and also tried to make the Iron Throne an elective monarchy, but I couldn't manage to get sufficient votes (none of the paramount lords seem to make it to the first three position).
There is some way to make a claim or I am permanently struck until I convert back to the Seven or the Old Gods?

 

[Rubidium]

If you're cruel (or some other traits, but you definitely can't be chaste, just, or kind, as those overrule) you can forcibly visit the chambers of a prisoner. Just be aware that it will seriously anger her family. Likewise with a slave (since an independent Rh'llor king I believe has slavery as an option). You can also try to fight your way to independence, and then launch an invasion of the Iron Throne through the "expand your realm" ambition, although that will probably require you to be much more popular among all your vassals.

 

[Cassilda]

I also tried the independence path, the main problems is that the Iron Throne gets an automatic de iure casus belli on Westeros, but the AI considers your character a rebel leader even after previously winning the independence (but I'm sure this is a bug), so, most of the time, if you can't beat the Targaryen easily, most of your vassals will switch side en masse.
I will try to kidnap a princess when I will have a ruler with the (im)proper traits.