You are asking the 555 to do something it was built from the ground up not to do.
In order for a hysteretic oscillator to work, there must be something in the circuit that responds to each transition direction. In a CMOS CD4093 gate or an opamp circuit, there is one comparator with a reference voltage that changes based on the output state. In the 555, Hans separated this function into two comparators, each with a different fixed reference voltage, but the function is the same. Indeed, for the 555 astable circuit the two inputs are connected directly together for this reason.
Separating the standard arrangement into two inputs, each sensitive to only one signal direction, gives the 555 its unique flexibility. The Threshold input responds to a positive-going voltage, and the Trigger input responds to a negative-going voltage, and there is not much you can do about it when driving the Trigger input. The 555 internal schematic is not super complex, and you can track the effects of voltage directions through it. Notice that the threshold input stage is all NPN transistors, while the Trigger input is all PNP transistors. This alone implies which signal direction causes action, and is confirmed by the Simplified Schematic on page one of the TI datasheet.
TI NE555 Datasheet