Very jazzed for you and this great trip you're planning. Hope yours is as good as mine was.
As an XR650L (with hybrid tires) backwoods veteran I can tell ya that there ain't no easy way and one techinique does not work everywhere.
Sometimes, like you said, get on the gas and stay on the gas. On an XR, in the really thick stuff, this is combined with the classic knee clench and lean waaaaayyyyyyyy back. Okay, now lean a little further. Get that back end to dig in and whisk you past the nonsense.
Other times when your ground speed is low ya gotta really work the bars and stay light on your feet. Use that KR grunt to pull you outta trouble!!!
The common thread here is that you have to concentrate a whole lot harder than some kid on a KTM, and, unfortunately be prepared to crash. This leads to the next chapter, bike fortification, one you already seem to be familiar with.
Use these last few weeks to keep working out and train as much as possible. A tired rider is an unsafe one!!!!!