No, you're wrong, and everyone else agrees on it. Really, why don't we just drop it, you keep believing what you say, and we what we say, and we'll agree to disagree. If we keep going, it'll get to the point where you realize you're wrong, but you're too far into the "debate" to agree you're wrong, so you'll keep trying to rig the Physics. So let's not.

But as for why you're wrong (if I didn't explain, you'd be sure to ask, and the argument wouldn't be dropped), it's because of what work is, which you've seemed to overlook.

The situation CANNOT be considered a change of reference frame, as you claim, and the bike cannot be replaced by an airplane or a hovercraft, unless you complicate the situation further, which is simply counterintuitive. So, lets stick with the bike.

W=Fd. I think we can agree on this. But that d is the distance the bike travels with reference to the ground, NOT the air/wind around it, which you seem to have claimed (correct me if I'm wrong, your explanations are a bit hard for me to follow). I mean think about it. If you're not moving at all with respect to the ground, just standing there, in a 20mph headwind, surely that's not the same as moving at 20mph at no wind when it comes to "effort," work, which is what matters. The work in one situation in the first situation is 0, in the second much more. And if you even remotely try to hint that the two are the same, I'm done with the conversation. No point to keep going.
And so, if moving at 0mph in 20mph headwind is not the same as moving at 20mph at no wind (with respect to the ground), then moving at 10mph at 20mph headwind is not the same as moving at 30mph at 0mph wind. And since the first is true, so is the second.

Now, case closed? Please?