Here's some pointers:
- go to your room every week to see his event
- invite him to one of your events (he won't come, but it boosts romance I believe)
- finish the historian secret chain and see the last one before the auto-triggered conversation with Jasper in week 4, then pick dialogue choices telling him to put down his burdens and assuring him you'll save the summit
That should help you get on his route. For the best outcome you have to have legendary endings for all countries. I think a perfect acquittal for Imogen also helps, in boosting relationship if nothing else, but I'm not sure about that.