Another alternative to bridges we don't blow is to make them impassable for vehicles. I'm not sure what the OS has fielded so far in terms of armor, but making the branches too uneven for treads, wheels, and walkers could go a long way in cutting down what they can throw against the walls and into the compound itself.
We can also use the Oversight recon droids to harass them behind their lines and while attacking, as they're fairly small. Not heavily armed, but enough to keep their heads low in large enough numbers and continuous strafing from multiple quick-moving sources in addition to any Wookie air support.