Thinking about it, the entire issue of 'Qyzen wouldn't date the person he basically believes is a god(dess)' isn't as much of an issue. If anything, it explains why he would be attracted to the Consular in the first place - come off it, if you had the chance to date a God, would you say no? Ignoring the whole potential smiting if you break up and such...
Qyzen would sure likely be scared to act on his attraction but if the Consular reassured him it was okay, he would be fine with it, because he wouldn't think the Herald would lie to him in attempt to put him in bad favour with the Scorekeeper.
The issue of anatomy doesn't really affect me in the slightest since I doubt it would ever be implied in the story that anything of that nature occurred. They likely wouldn't even kiss. Notice how the Khem romance was going in for the kiss as pulled a 'hah, you thought-'. A romance doesn't need to include that kind of physical affection to be a romance.
Kids aren't a problem either if we consider the fact that this is a Jedi and shouldn't really even be having kids in the first place. Qyzen/Consular couple would be more the kind to get a puppy anyway, I'd imagine - although Qyzen would take a lot of convincing.
The Wookie pelt - Qyzen technically already gave the Consular a Wookie pelt, with the intent for them to give it to their romantic partner. The Wookie's already dead. It's not like the Consular can un-kill the Wookie so. Absolutely a light side Consular would encourage (or attempt to encourage) Qyzen to drop the whole Wookie thing but it's not like he's saying he would go out and kill a Wookie for them. It just so happens that he has a pelt from a pre-deaded one. Also totally just headcanon here but the idea of Qyzen giving the Consular the pelt to give to their romantic partner, only for the Consular to then later give it back... Cute.
Then again, an awful lot of this stuff likely wouldn't get much fleshing out, it would likely be a case of one scene and be left on pending forever, much like Khem, and I'd honestly be okay with that. Sure, more is better, but just having it be available to be an option of 'Sure, you're dating Qyzen now. That's your official romance in the game' would be enough because the Jedi Consulars, particularly female, did not get the best lot in life with their romance options in the first place, just give us something for the best companion in the game.