I would paint all of the ceiling trim the same shade of white as the ceiling. The window and door trim can be the same white but should be a semi gloss, and the ceiling can be a flat paint. I would use a light bright white.

The walls can be a creamier shade........

I would leave some wood for flair. You cannot make a post and beam log home pretend to be something it is not, thats the charm. Having said that have a look at the newest Canadian House and Home magazine, featuring a post and beam in North Vancouver, see photo 1.
Other options, see photos are less drastic, just more a decorative approach.
Whatever you do I would not leave the trim a different colour, it will look strange and confusing, as in if you are trying to frame something negligible, the attention should go to the walls, the ceiling or the beams, not the trim.
If you want loftstyle and maximize space, I would use one white throughout. Be careful though, as a fellow BC resident I find it difficult to find the right white for a certain location and exposure, some whites will look very dull and even gray on those gloomy days, or shall I say weeks? Try different options on your walls, view them different times of the day and n different wx, then make a paint colour decision.
Best of luck!

This was the first time I've used Houzz for advice and it really worked! I got exactly the advice I needed. And don't worry Mveasy - there is still going to be plenty of wood in this house. We just the the logs plus the ceiling, handrails, accents etc was overkill and too dark. We'd like to show off the nice wood and make the whole place brighter. Thanks again!!