Right on, Barit!
You make a very good point here. But it still seems to make more sense to have the "fan" stages feed a classic circumfirential duct, allowing both the harnessing of that airflow for "propeller" thrust at low speeds, i.e. dragging a full fuel load off the runway for once, rather than just enough to allow one to clear the runway and scramble to the nearest tanker, and then allow the air exiting the fans to simply follow the "path of least resistance" in the intervening space between the low and high pressure sections, flowing into the N2 as needed and going around through the fan duct when either quantity or pressure are in excess. Also, noting the degree to which the French aero engine industry, specifically SNECMA, has benefited from liasons with BOTH(!!) GE and P&W, I'm surprised and a bit disappointed that that "river" could not flow the other way as well, a "J-58-as-scaled-up-M53" still looking extremely good as the quintessential Mach 3+ powerplant.