How do I get into Le Biochambre 4000?

Hint 1 of 8:

Cecil is standing in front of the control panel to the chamber.

Hint 2 of 8:

He's not going to let you access it right now.

Hint 3 of 8:

But you might be able to convince him.

Hint 4 of 8:

Or change his state of mind.

Hint 5 of 8:

Hypnotize him.

Hint 6 of 8:

Use Al Phee's beanie to do so.  Cecil won't actively cooperate once you do,
but he won't stop you any more, either.

Hint 7 of 8:

The proper sequence of buttons on the panel will open the door.

Hint 8 of 8:

Although there appears to be a way of solving the puzzle without trial and
error, I found it easier to use trial and error than to solve the puzzle the
intended way.  Read ahead for the solution.