I don't follow this. The 1000 point relay should only pulse briefly and should only score 1000 points when it does. To score 3000 points the 1000 point relay needs to pulse three times.

To score 3000 points the 3000 point relay needs to pull in and hold while the Score Motor turns and the 1000 point relay pulses three times. Then the 3000 point relay should relax. If it's not doing that try to manually push in the 3000 point relay. It should hold itself in for most of the 180 degree rotation of the Score Motor.

/Mark

That's not right.
Old Chicago 3000 points (resized).jpg
When the 3000 point relay fires it holds itself on, closes the lower switch in this schematic and starts the Score Motor turning. The 9B Score Motor switch in red then closes three times as shown in the Score Motor chart which should send three pulses to the 1000 point relay for 3000 points.

If your 1000 point relay stays on while the Score Motor turns it may be that the Score Motor 9B switch is stuck closed rather than pulsing as it should.

https://pinside.com/pinball/forum/topic/sky-kings-power-free-play-and-top-hole-issue#post-4457680 will show you were the 9B switch is.

My experience may or may not help you. Mine would never score more than 5K in bonus. Anything over that you earned up to 10K was just ignored during the bonus count. The unit would still fully reset, but didn't give you the points. Everything was cleaned/gapped/lubed properly on the bonus unit. I had forgot to clean the jones plugs in the bottom of the cab that connect the playfield to the rest of the game. Cleaned them well and retensioned the female receptacles and my issue was resolved. Not sure how recently you shopped or cleaned yours, but may be worth a shot.

As it turns out that's correct. The 3000 point relay isn't used when you land in the Collect Bonus hole. The Bonus has its own circuit:
Old Chicago Bonus count (resized).jpg
The Bonus Unit is probably an 11 position stepper where position 0 is reset and positions 1-10 correspond to the letters O-L-D-C-H-I-C-A-G-O. Each position sends pulses to the 1000 point relay generated by various combinations of Score Motor switches for totals of 1-4000. Bonus values of 5000 and more start by counting 5000 points (done elsewhere in the schematic) and then adding 1-4000 more points from this circuit.

So for example the first letter O in position 1 should send a single pulse from Score Motor switch 3C to the 1000 point relay. The L in position 2 would send the pulse from Score Motor 3C and the pulse from 4C to the 1000 point relay for 2000 points total.

If letters D, C, A & G (or positions 3, 4, 8 & 9) are missing 3000 points I'd have a close look at the Score Motor 9A switch in red.