I'm unsure of the answer to this question, you will need a knowledgeable 747 driver or dispatcher to answer this (not one of the ACARS wonders who just follows what the box says).
The 737 example is invalid, that is a 737 and it behaves like a 737, not a 747. You will find that aircraft with more than two engines do not suffer as drastically from greater flap extension, as two engine aircraft do.
The climb limits are based on one engine out at the most critical point, on a 737 this is a tremendous loss of thrust. On Super 727s (2x JT8D-17 and 1x JT8D-217) your climb limits will usually not be a factor regardless of flap setting (even at 30* the climb limit still exceeds the maximum structural weight).
Now, I have not flown 747s, but to get the correct answer someone who actually knows the performance characteristics of the aircraft would need to chime in. I would not be surprised if even Flaps 20 would not be limiting under normal/average conditions.