...that Jane believed enough in Frank to expect him to gradually bring the subject up with his foster parents, and if he found them adamant, look for a way to support himself and Jane after breaking with them.

As we see, there's no evidence at all that Frank had enough awareness or integrity to actually do this, so that even if he hadn't misbehaved so abominably at Hartfield she would have had to break it off eventually -- and I think (with no more evidence than my own high regard for her character :-) it would have been soon, though not so soon as Frank's behavior forced.

If Mrs. Churchill's death was a cheap plot trick, it seems to me Austen went to a lot of trouble to prepare for it. Mrs. Churchill was described throughout the text as being sickly, and we have only Mr. Weston's sniping to counter it -- a man who, as far as we know, has not been to Enscombe or met Mrs. Churchill since he left Frank with them (if even then), and who nurses a harsh grudge against her. Yes, her death was not obviously related to her complaints, but poor health can be misleading in character, and can provoke other problems not obviously related to the specific sickness.