Various thoughts in no particular order ...
I don't think you want to bother with much (if any) cavalry. Once the enemy has rifllemen, the age of cavalry is over. Maybe a few quick response troops would be useful, but you're not going to get any significant attack value out of them. Make cannons, grenadiers, and riflemen.
If you're going for diplomatic, you might as well accept capitulation from Tokugawa as soon as possible (note: I sort of change my mind on this later in the post). Take any cities with wonders or really good resources, but you'll get his votes automatically if he's a vassal. Also, if he's your vassal, then you don't need to take his cities in order to get access to your new, formerly Japanese cities. You have free passage through your vassals' lands.
As far as diplomatic goes, your continent will get you most of the way. Research Biology quickly and immediately gift it to Tokugawa to help boost his population. Also give it to Ragnar unless you think he's in danger of becoming your rival in the elections (though it might not matter, since he can probably research it himself easily enough). If you do a lot of farming and beeline to Mass Media, you can probably get by with only one of Alexander or Isabella voting for you.
How do relations look between Churchill and the other civilizations? You're going to need to shore things up with Alexander. Free Religion will probably help, but will it be enough? How much of a ding are you taking from Alexander and Isabella for religious differences?
Favorite civic is the other obvious way to get points. That's going to be a tough one with Isabella, because hers is Theocracy. That's a damned if you do, damned if you don't proposition. Alexander loves Hereditary Rule, so you might want to consider adopting that as you close in on Mass Media. You want to do it late enough that you don't hurt your economy, but you need to do it early enough that you accumulate some long term love.
It's going to be a lot of screenshots, but it would be really useful to see the detailed diplomacy information (the full +/- popup) for everyone with you and everyone with Churchill. Also the general attitudes toward Tokugawa (because you want to see if anyone will get mad when you redeclare war).
Keep in mind that vassals get you a -1 with everyone else. They don't like your influence. So that might be a reason to consider just wiping Tokugawa out. Without knowing the full diplomacy information, my intuition is that it's going to come down to Alexander. If you can swing him over to your side, you probably win. If not, forget it. That might be a really close call, and the extra -1 might be the deciding factor.