These modes are very long and without checkpoints it's painful when things fall apart towards the end. I've beaten Baghdad Mayhem and got to the end of Tokyo Raid, but I have very little desire to play either of these again. Knowing that one little mistake might destroy an hour's worth of progress is not fun.
It seems like it would be reasonable to have a checkpoint after you complete each stage. If you're worried about having something that is more of a challenge, maybe you could make a "hardcore" version these that doesn't have any checkpoints, just like before.