I'd put white beadboard over the rafters then paint em white.

Water based aniline dye is actually very easy to use. The penalty is raised grain, but you can eliminate some of that by wetting the surface ahead of time, applying a wash coat of 1 pound cut shellac, then lightly sanding the surface. The shellac will mostly be removed, and what remains is so thin it does not interfere with the dye. It also helps with woods prone to blotching (pine, cherry). Cover the surface, allow to sit a few minutes (with so much there is liquid on the surface), then wipe off the excess. Allow to dry. You need to mix the color you want, since adding another coat will not appreciably make the wood darker. I use a scale that can weigh in grains (1/7000 of a pound) to mix dye at known concentrations for testing. Say 100 grains in a quart of water. Test on a small piece of the project wood. If it is not dark enough add a measured amount (say 50 grains more) more to the quart and try again. When the color is correct, make as much as needed up. A little more than you think you will need is a good idea, but if you weigh carefully you can make another batch that will match. It is the extra steps (wash coat of shellac, light sanding, etc) that the various stain products try to eliminate. There are 'non-grain raising' aniline dyes available. They use alcohol (or even oil) as the solvent instead of water. They tend to dry so quickly getting an even coat is difficult outside of a factory using spray equipment. Moser has a large assortment of water aniline dye available from a number of vendors. There are both mixed ('cherry', 'golden oak', etc.) and raw colors (burnt umber, burnt sienna, etc.) available from the larger vendors. There are even color wheels available to mix the 'standard' colors (like cheery or oak) from the base colors. You can tweak the mix to your liking.

I would contact your local architectural historical preservation organization... They will know your neighborhood and your house's style, and should be able to give you trusted information. :-) Alternatively, if you know any architects, I'm sure they could give you a quick answer. Heck, for all I know, it doesn't matter whether you paint or stain, lol, but with historic properties, it's always best to ask before doing something!

I am having a similar dilemma, so I would love to see what you end up doing. I have always thought this room to be very pretty and although you are doing a dining room, they are similar: https://www.houzz.com/discussions/love-this-ceiling-is-it-tongue-and-gro-dsvw-vd~21695 We have a designer here in Canada by the name of Sarah Richardson who likes to whitewash a lot. I recall one time reading that to avoid a pink look over wood that some whites leave, she actually uses a gray paint and then wipes it off. Maybe not wipe so much of the paint off on your sample? It's a lovely room and with that view is bound to look gorgeous no matter what you do.