You are correct that the door's state is saved in the savegame. However, it is more in the realm of level-editing than save-editing, so you'll need ERF Edit and K-GFF.
You'd open the SAVEGAME.sav in ERF Edit, extract the level's .sav file from the SAVEGAME.sav, then close ERF Edit and open the level's .sav file in ERF Edit.
Extract the .are, .ifo, and .git file. In either the .are or .ifo, there is a PlayersList or something like that that will have one struct containing your PC's info. Of importance would be the XYZ coordinates. After we have those and they're written down somewhere, we can go looking through the .git file.
When you open the .git file, I recommend clicking on a branch and then hitting the [ key to collapse everything. From there, open the DoorsList and look through the structs until you find one whose coordinates are close to your own, assuming you saved right next to the door in question.
When you find the door, I'm blanking on what exactly needs editing, but I think AnimationState should be 0 for closed. Might also need to re-lock it by setting Locked to 1.
After all that, click on a different branch, save the .git file, put it back into the .sav file for the level, then put the level's .sav back into SAVEGAME.sav. If you need help, just ask.