That's a tough one. Get a good brush on your vacuum and use that. My fiance has a log cabin. It really is the best way to clean logs. Just vacuum them.
a bit of trivia, although chinking is the commonly used term, I learned thru the historic state fund, that the term dobbing is the correct term. The fund shared that chinking is the scrapes place between the logs to hold the dobbing in place.
I never took a picture of the interior.
how did I post this picture, there is horizontal icons above. The second icon is for photos that will help you step by step.
Those are hand hewn logs. Don't use a wire brush - you'll crape the wood.
I have a log home - I know how to care for them.
remember, water is the enemy. I wouldn't go any further with water. especially in the inside. those logs don't look sealed, and they wouldn't be on the inside. be very careful when it comes to water and wood.