Just because the training organisation in question says they don't think you have what it takes does not mean you can't be a pilot. I know the company you are referring to very well (I am just doing my IR at the moment) and as much as I don't have any issues at all personally with the training I have been given, I know some people who like yourself, have not gone through at the same pace as others for a number of reasons, largely down to having instructors who aren't proactive enough and really really bad luck with weather! As you say, the nature of the scheme is such that they need the trainee to be complete to the standard in a certain time period, and given how tough the selection is and how much further than the bear licence issue minimum standards the training takes you, perhaps means that this is not a conventional method of becoming an airline pilot, but rather a more intensive programme. They require the finished product to reach a minimum standard if the relevant airlines who take us on are going to stick around. And Hufty, you definitely are not the customer here! The contract basically says so, but they quite clearly tell you this throughout selection before you sign on the dotted line.
Perhaps Integrated is not the way forward - think as others have said about modular (try to do one-stop modular though). Having the drive to get there is one of the biggest hurdles. If you can get onto a scheme like this in the first place, you are clearly qalified and have the right personality. You just need the right instruction to get you there, so shop around.