This is your first student going up? Good luck!

What you describe does raise a flag. 100 hours to PPL might not be significant if the guy was really busy and could not train consistently.

But do you know why he had seven instructors? If he's been working on this for five years, maybe they all just moved on...but there hasn't been a lot of movement lately...

Unfortunately as an airline-bound instructor you need to be concerned about you pass rate, maybe a little more so than other CFI's. Some airlines will use that as a measure of your suitability. You need to log that, but I suggest you don't do it in your logbook, put it somewhere else. That way interviewers won't have automatic access to it. They might still ask, and might insist on seeing your records but if you don't end up with the kind of pass rate you would like (90%+) no need to hand that over unsolicited.

I have an issue with that, because it is possible to "cherry pick" students so that you don't have to deal with challenges and can be assured of a high pass rate. Kind of like a doctor selecting only patients he can treat successfully...

I think you have something of a professional obligation to train all comers (assuming no personality conflict or other such issues). But you as an instructor are NOT obligated to sign someone off just because they have invested a ton of money into training.

If I got a student with this guy's history, the first step would be to analyze and discuss what got him in the situation he's in. Try to identify things to change so that his training with you can be more successful (consistent training, more studying, chair flying, listen to ATC on a handheld, etc).

Once training begins if I realize that the student is making slow (or zero) progress...have another chat, and at that time mention that a sign-off will not be possible unless things change. Keep reminding the student as things progress so that it will not come as a surprise at the end. I had one student who completed an entire IR training program, but she never quite mastered communications with ATC. I kept telling her that she had to master that too, and assumed that practice would et her there. In the end I never signed her off because she would get overwhelmed by complex instructions such as holds and even instructions to fly a heading, maintain an altitude, and intercept a localizer. Other than that she could fly fine. Sad situation but at least she had been warned along the way. Of course there was no way I could turn her loose in the system...I thought about sending her up for a ride just to see, but I was afraid that she might pass if the DPE gave her simulated ATC instructions...it was real ATC that gave her more trouble.

Tough deal, but it does happen. Make sure you give students honest progress evaluations, and if you spot any show-stopper weaknesses be sure the student is aware that is a no-go item for a sign-off.