I would try two things in combination:

1) Flash the paper
2) Do a split-contrast print

Burning in, is really hard when you have a lot of branches and stuff like that, flashing and 00-filter should get you a long way salvaging the highlights as much as possible, maybe even in combination with a dodge on the darker parts, as you'll probably need quite long exposure-time with the 00-filter to salvage the highlights.