Both my Boxsters have this problem, the one I am selling is the worst. I decided to fix them both starting with my 2000S, that I am keeping, to gain experience before doing the one that is for sale.
The video from Help Me DIY is my inspiration:
https://www.youtube.com/watch?v=42IZ0lb33C8
Some things that I did differently.
1) Instead of cutting the sides of the snorkel-like duct and folding it down I cut the bottom as well and removed the cutout completely to simplify the operation and have more room.
2) I worked with the first door partially or fully open rather than fully closed as shown in the video. This gives more room to get a hand in to remove the old foam and the access to the door is just as good.
3) Instead of using tape or foam I used a piece of thin aluminium that I JB welded to the door. The advantages of are that the aluminum is easier to control than tape when maneuvering it into place and before the JB weld hardens the patch can be slid around to place it accurately. With the door fully open it is easy to feel how the patch is placed at the bottom and on the sides.
I stuck a couple of pieces of masking tape with a fold in the middle onto the patch to act as a handle during installation.
The second door will not be so easy. The foam on it is starting to degrade but is almost intact and very resistant to being removed. I am considering the alternative of going in through the heater core which gives better access to this door. I can wait to do this later, so will button up the parts that I removed and come back to it some other time.