This is quite an interesting and vocal thread. Here's my two cents worth:

I think all sides have valid points on the pros and cons of Germany invading England. On paper, invading England would be a plus for Germany but in reality, Germany didn't have the resources to properly mount an amphibious operation in the scale needed at that time. That's historical fact.

Now I respectfully disagree to the views aired that a country without any amphibious ops experience cannot learn how to do it. It's not out of the realm of possibility for Germany to learn how. The problem would be on how they would go about in learning the basics of it.

Sea Lion in its basic form wouldn't work. But I do think that tweaking the plan, plus a little creative thinking, another way could have been found to mount an invasion of England within the resources available for Germany. Of course, I say this in the context that Barbarossa will not be mounted.

The basics of the plan I think that might be workable:
Germany raises the scuttled French fleet and use it.
A sustained aerial campaign on British bases and installations in England (ignore the cities) while developing better aircraft to deal with the RAF.

Germany military observers study the ongoing Pacific campaign. They could learn a lot from it. That's not impossible to do.

In short, invading England is not out of the realm of possibility. I wouldn't say this would succeed but it would increase Germany's chances of succeeding.