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Do you want the RAW or the RAI answer?
As Written, it is a 35 DC. Invisibility gives you a +20 and that's just that.
As Intended, it is a 15 DC. There's no reason invisibility would make you quieter.
Invisibility makes it more difficult for the Guard to perceive you. Arguing intent in this instance is a slippery slope.
Your reasoning for a DC 15 check is, reasonable.
It would also be reasonable for me to say that creatures that primarily rely on sight; such as the Humanoid races, put so much emphasis on what they see, they don't utilize their other senses enough. You've heard the phrase "seeing is believing"?
In the case of invisible creatures it's not unreasonable to say that because they cannot be seen, they are much harder for Humanoids to detect.
Hence the reduced modifier for an invisible creature who is also moving...