Salute!
I'll stick with the SR-71 manual and other sources that the J-58 never quite got into a "ram jet" mode at all. It simply bypassed air from one of the compressor stages when the "core" engine couldn't use all of it efficiently, but the burner could. Let's face it, the core couldn't handle all the air and then we had temp problems down stream.
So the extra air from those bypass ducts in the J-58 allowed the burner to work really well. Lottsa air and somethat cooler that that going straight thru the core. We saw this in the F100 motor from Pratt in the Eagle and Viper. The difference in burner thrust was a much higher percentage than with the older motors that simply added JP-4 to the air that had not burned completely going thru the core and the turbines.
The problem with our fan motors was instability in the bypass duct, which was not like those tubes in the J-58. So think another ten years of design and knowledge gained from the J-58. We never had the classic compressor stall effects - loud and physical bangs or chugs. We would have an unpooling motor and "torching" out the burner nozzles, and associated loss of thrust - called it "stall stagnation". Pratt worked on this a lot, and I think the solution was in the nozzle control. BTW, our initial Viper squadron tech rep from P&W had been involved in the J-58 design and testing.
The only Blackbird pilot I have discussed this with said they "inlet unstarts", and whoa! Lottsa loss of thrust from one side and it required some good ruddeer and other "pilot things".
One of the more intriguing designs would have had the spikes at the inlet and the geometry of the engine close down the core airflow even more than the J-58. An annular bypass and not a half-dozen tubes as the J-58 had. In other words, an F100 type motor with a fancy inlet spike as the SR-71 had.
We got by just fine, thank you. That fan really helped with range, and I had flown the SLUF with the TF-41 for a thousand hours and it worked the same.
Great discussion here,