I beelined for Jasper first as soon as the demo came out and also aimed for him first as soon as the game got EA, and I can confirm that you don't need to finish the historian chain to successfully romance Jasper, but the ending is definitely a lot happier if you do (yup, I totally went back for him multiple times). To unlock his epilogue though, you need to finish the historian chain AND complete some legendary requirements, which I have yet to do. Like the previous post commented, visit your room every week, be nice to servants (stand up for Sarya, offer them your breakfast, etc). For Imogen's trial make sure you ask him why the head butler won't let you question Imogen, BUT make sure you don't push him for more info a little bit afterwards when you notice that he is tired and invite him to sit down and talk with you.