ref Megan's original question :
"at cruise, the rotor of the engine actually has a small negative thrust load on the engine" from Richard Graham's book . He was obviously repeating an explanation from someone else, ie would have been second or third hand, perhaps with a bit of miscommunication thrown in. Ended up confusing rotor thrust with engine thrust, which some people do. They say, big fan engine for example, most of the engine thrust comes from the fan but then presume it comes through the fan rotor thrust bearing. Except airfoil aerodynamic load contributions to total rotor load are not necessarily the biggest nor in the same direction.
More to the point FWIHR J58 bearing skidding only occurred during windmilling . Also the follow-on supersonic cruise engine, JTF17, design had to be based heavily on previous high mach experience , ie J58, and would have had 4,000 lb forward at M3, 70,000 ft.
So, should he really have said engine load was rearwards? in which case he would have been repeating what David Campbell says in next line. He was Ben Rich's man on propulsion system and inlet patent holder.
"at M3+ if afterburner reduced to minimum engine would be dragging on engine mounts" ie t/mc was actually a drag item and needed more than min a/b to provide thrust through mounts.
The effect of a/b setting from an internal thrust imbalance pov is given by "converging engine nozzle is a drag item. Afterburning allows nozzle to be opened up which reduces rearward load and this is the origin of thrust boost, ie internal thrust out-of-balance ( = engine thrust) now has a reduction in one of the rearward contributions" RR book
Or conversely closing down nozzle, as in first line, increases nozzle drag so engine is now dragging on mounts.
We would expect a turbojet to run out of thrust when reaching a certain speed, on paper that is, "for a turbojet engine, depending on compressor pressure ratio, ram recovery and turbine inlet temperature,
thrust drops to zero at M3+" NACA performance study. ie needs an afterburner
And it looks like the J58 t/mc had already ceased to be a thrust producer at cruise (not withstanding its bleed-tube-enabled increase in compressor mass flow and hence thrust) in so far as its pressure loss meant it didn't contribute to a/b nozzle pressure ratio "J58 t/mc
pr 0.9 at cruise" ( P&W engine/nacelle total pressure schematic avail at enginehistory.org)