I doubt flipping the wires around will change this issue.
Anyway, from what little information I could find, I think an Omron G5LE-1 DC9 may be the equivalent.
How sure are you about this replacement? I can't seem to find any information on the Millionspot H200S09 relay.
The screwdriver is a triangular tip, I made mine grinding down an old Phillips head screwdriver since I didn't have the actual screwdriver.
Click on graphic to enlarge.
In the schematic, both U1b and U1c are amplifying the current sense signal. U1c, the "overload" detector, has a gain of 148, but it is slowed down by the resistor and capacitor on its output. The time constant (RxC) is 2.6 seconds. Multiple short hits to this RC combination would charge it up until it trips the relay latch.
U1b has a gain of 37, which means it requires 4 times as much current, but it acts instantaneously for "dead short" situations.