"With" doesn't work because that suggests an ongoing job:
With all kinds of difficulties, they're making rapid progress......
"For" simply doesn't work at all.
After all kinds of difficulties, the workers have made rapid progress.....
This makes much more sense. There were a lot of difficulties at the beginning, but once the difficulties had been overcome, the workers were then able to get on with the job and have made rapid progress. They could only make rapid progress "after" the difficulties had been dealt with.
Student or Learner