I understand the reasons for Midnight were less about budget constraints than that Catherine Tate was unavailable as she was filming on Turn Left - an episode very Donna-heavy - so they needed to come up with a story that focused on the Doctor alone and used CT minimally. Hence, CT only being in the first and last scenes.
Like I say, I get that it was supposed to be a deep psychological study, but it just didn't work on that level for me and that was mainly down to what was, imo, a very clunky, unoriginal script from RTD. I can't fault at all the acting in it, which was very well done from all concerned. And it's a pity because those kinds of psychological episodes are often great favourites of mine. I usually would have enjoyed this immensely, if it had been done with a degree of flair.
Interestingly, aside from the first and last scenes with Donna, which I've already mentioned, the only moment in the entire episode which did work for me and which I did like is the one you cite, Terry - where no one knows the name of the heroine who saved them.
LabRat