I know I haven't helped as my post alluded to the whole integrated/modular debate but I would say lets avoid getting into the debate here since chuckerofspears wasn't really asking for that debate.
I will just qualify some of my answers so as not to appear so naive for you.
Where did you find this out from, Wazzoo? Do you realise how many hundreds of potential employers there are out there? How few even express a preference, let alone the fewer who operate one practically? How few new graduates those few airlines take?
I realise there are a huge number of employers out there (regional TPs, cargo TPs, instructors, paradropping, bush flying, aid flying, the list is endless), and also that jet pilots are in the minority. Sorry if I jumped the gun in dismissing them all in one go. However the reason for dismissing those was chuckerofspears situation in that he's approaching 30, looking to get into the industry as quickly as possible. He probably can't hang and pick up random jobs here and there building up the hours, and most likely wants to get into a semi-secure job that pays well soon.
With that in mind, he's probably limited to jet airlines and regional TPs. Of which some have expressed the prefference for integrated students. Certainly you can say that you're not gonna get one of those lots saying they won't take an integrated student where some do go as far as saying they won't take a modular student.
"It may mean you are on TPs for the first few years before getting a break into Jets..." is a very naive thing to say, suggesting that jets are the only thing out there. If that's your attitude then I suggest you save your money, find a lucrative job with cheaper training and more certainty: if you truly want to fly then you either wouldn't care (as spearchucker seems not to) or you would actually see jets as the final let down,
Again, see my coments above. Certain peoples situation restricts them from going off galivanting around the world picking up different jobs. Or even hopping from one small time TP to another. Jets arn't the only thing out there, and i know I have dismissed a lot of the industry with my comments but I know for myself that I have to rule out certain options. I don't have the luxury of being a single person able to go anywhere at a short notice and pick up anthing that comes up. I'm happy to admit that my end goal is jets and that I'll be looking at probably trying to pick up work with on TPs to begin with but soon move up.
As with so much with learning to fly, whether its a debate about degrees and education, integrated or modular, CCAT or OAT or another place nine times out of ten it will come down to your particular circumstances. There is no one size fits all answer. I only hoped to try and address chuckerofspears particular situation.