8 Romances, all companions + advisors? Let's see here...
1. Josephine - Female Bisexual
2. Cullen - Male Straight
3. Cassandra - Female Straight
4. Sera - Female Homosexual
5. Dorian - Male Homosexual
5 confirmed, 2 male and 3 female. 3 remaining. Among the remaining companions, since Cole is all but confirmed as not an LI, the remaining LIs must be from:
1. Iron Bull
2. Varric
3. Viviene
4. Blackwall
5. Solas
I personally rather doubt Blackwall, as he seems more like a grizzled mentor figure. I'm not sure about Varric because I have a tough time imagining him leaving his position as the hero's "bro". Iron Bull seems likely and I have no idea about Solas. One thing's for sure, Viviene has to be an LI if they care about gender balance at all. As for orientation, if they go for a 2/4/2 spread, the last 3 LI's could all be bisexual. Then we'd have 2 straight (Cassandra and Cullen), 2 homosexual (Dorian and Sera), 2 bisexual females (Josephine and Viviene), and 2 bisexual males (2 of the remaining men). Then there's plenty of options for every Inquisitor! So my best guess:
1. Iron Bull - Male Bisexual
2. Viviene - Female Bisexual
3. Solas - Male Bisexual
I won't even begin to speculate on which 2 are race gated.
EDIT: And now I will! Maybe Iron Bull won't be interested in dwarves for practical reasons. Maybe Dorian won't be interested in Qunari because he's from Tevinter. Maybe Sera, being a city elf, has chip on her shoulder about humans she can't quite get past. I'm not sure what reason the others have to be super picky, they all seem fairly open minded (Race-wise anyway). I doubt Viviene would let a little thing like race get in the way, she seems too ruthless. Cassandra, well maybe she would have a problem with the dalish Inquisitor being a practicing heathen, but I have a hard time imagining that being more than a speed bump if she really wanted it. She's quite strong willed and certain in her principles, but also a romantic. Josephine... albeit, we don't know much about her but she is Antivan, they're not known for their dedication to propriety and whatnot. I don't see her being so picky. Cullen would probably be more concerned over the PC being a mage or not rather than her race. Everything we've heard about Solas indicates him being extremely open minded, I don't see it.