Pulling up on the cover worked for me too. I found that the best place to pull up on the cover is at about "true north" in the picture ... near the black dot used to indicate lid-is-closed. I did it before installing any screws and all four screws went in fine.
The new drive, being thinner than the old one, was a bit tricky to get seated into the rubber grommets. I found that temporarily screwing a couple of screws into the top mounting holes on the drive helped with getting a grip on it. This, and standing the unit up on its end so that the drive would "fall" into the rubber grommets, worked OK for me.
Peeling the bar code sticker worked for me. The bar code sticker remained intact with the heat sensor still stuck to it. Be careful to keep the bar code sticker fairly low while peeling it because the heat sensor board is very thin and will flex along with it. I did not remove the heat sensor from the now unstuck bar code sticker. The bar code sticker had plenty of stickiness to it, which allowed me to just stick it to the new drive, heat sensor and all. I first peeled the bar code sticker off the new drive just in case having two layers of bar code stickers messes with the sensor's calibration.
The pin method is definitely better. I used the pin to slightly spread the "wings" of the connector on the board. Then I levered out the part that is attached to the wires. All done with the aid of a magnifying loop.