I went the FBO route, so I can't speak first-hand about any of the training facilities in which you're interested. I can tell you, however, that any "established link", "hiring agreement" or "preferential interview" setup which any school may claim to have is not worth the paper it's written on - least of all in the current job market. I'm not sure how Oxford or any other academy on that side of the pond may work, but over here, such arrangements disappear at the drop of a hat.
I have worked with several people who worked with Delta Academy and Gulfstream. None of them had anything good to say about those establishments. Embry-Riddle is a respected 4-year degree course, but any talk of them being "the Harvard of the Skies" or "the fast-track to the airline world" is strictly marketing's hot air, often parroted by young pilots with misplaced priorities. Schools like ATP and PanAm seem to specialize in the kind of setup you're looking for, and I haven't heard anything really bad about either. PanAm seems to place more emphasis on international clientele, so they'd be the most likely to know all about the TSA hurdles you'll need to clear.