It's not completely hopeless. Ok the trust has 14 battle fleets compared to the 80-120 chaos battle fleets. Yes any chaos lord in charge will have to have a paragon trait but also Have orders to kill the tryanids. We have the advantage of being secondary target and for the orks to be attacking them if we can pull it off.In that case we die or hope Avernus can bail us out, the difference in scale between that fleet and our military is so vast as to make any improvements we might make insignificant.
About the only way I could see us even having the slightest chance would be mass suicidal assassinations of the command structure with heroes. Our forces are a rounding error to the Black Imperium's task force
Our biggest threat from the task force is if they can get enough time and force concentration to wipe us out. So the region being on fire is a good thing if the task force arrives.