There may be an easier way to do this, but the least invasive way I can think of:
get another relay, and wire it to trigger the bank reset. Then swap the P/S relay to trigger that relay instead, and also wire the kickout circuit to trigger the new relay?

I'll post this as a design exercise for educational purposes only rather than as a recommendation. The Target Bank Reset circuit runs at 120V AC so that's not something to mess with unless you really know what you're doing. Use this idea at your own risk.

Since the Target and Sequence Bank Resets are wired in parallel, you need to introduce a way to isolate them from one another to get them to act independently. You also need to preserve their existing behavior during during reset. Given those constraints here is one way that should work:
Bronco Target Bank Reset (resized).jpg
The F and G relays fire when the ball drops into the eject holes and start the Score Motor among other things. Both relays have 5 normally open switches already. In this design two more switches would need to be added to the F and G relays.

The upper red path shows that when either the F or G relay fires a new path would send power to the Target Bank Reset solenoid from the Score Motor 2C switch through one of two new normally open switches. The lower red path shows that when the F or G relay fires the path to the Sequence Bank Reset solenoid is blocked through two new normally closed switches. All four switches would need to have large, high current contacts.

The existing wire into the Sequence Bank's 1/2 amp Slow Blow fuse would need to be cut and the two new NC switches added in the gap.

Note also that this schematic was generated from the export version of the schematic, not the domestic version originally posted so the transformer configuration is slightly different. The circuit changes however should be the same.

/Mark