I pretty much came up with the same way to solve the final corners
One thing that is nice about this puzzle is that it is so large you have a lot of room to experiment without effecting the area you are working on solving. If you are down to the final few pieces, turn the puzzle over and play around with some move sequences on some of the solved sides to see how the pieces move around. You should be able to find something you can apply (with the addition of some setup moves) to the area you still need to solve.
Another nice thing about this puzzle is that you don't have to worry about corner orientation unless you jumble.