Okay, so here we go. It's not necessary to follow the instructions exactly if you know what you're doing (if you know, you can most likely see the important parts yourself, so there's no need for me to list them) but if you don't, it might be a good idea to do as told here.
You'll need ErfEdit and K-GFF, both are available at starwarsknights.com.
1. Install TSLRCM.
2. Install M4-78 EP.
3. Make a folder somewhere to put your working files into. I will call it "working folder" from now on.
4. Make a backup copy of module "701kor.mod" to your working folder. Rename the backup to something that makes you remember what it is. I will call it "RCM_701kor.mod" from now on.
5. Run the Korriban Expansion installer. Don't use the TSLRCM compability file, we'll do the merging manually.
During the installation, you probably got a warning "global.jrl already exists in Override folder. Skipping file". That is to be expected and nothing to worry about - everything is as it should. If you get any other errors, however, something is wrong and you should not proceed.
6. Copy the 701kor.mod that Korriban Expansion installed (or pick the 701kor.mod from installer's "tslpatchdata" folder) to your working folder and rename the file to something that makes you remember what it is. I will call that file "EXP_701kor.mod" from now on.
7. Open your EXP_701kor.mod with ErfEdit and extract files "701kor.git", "new_701area_ent.ncs", "to_740.utt" and "wp_valpath.utw" to your working folder.
8. Rename the file "701kor.git" to "EXP_701kor.git".
9. Make a copy of your RCM_701kor.mod and rename it to "701kor.mod". Put that file into your working folder.
10. Open your RCM_701kor.mod with ErfEdit and extract files "701kor.are" and "701kor.git" to your working folder.
11. Make a copy of your 701kor.are, rename it to "RCM_701kor.are" and put it into your working folder.
12. Make a copy of your 701kor.git, rename it to "RCM_701kor.git" and put it into your working folder.
13. At this point, you should have following files in your working folder:
701kor.are
701kor.git
701kor.mod
EXP_701kor.git
EXP_701kor.mod
new_701area_ent.ncs
RCM_701kor.are
RCM_701kor.git
RCM_701kor.mod
to_740.utt
wp_valpath.utw
14. Open the file 701kor.are in K-GFF, find the field "OnEnter" and replace value "k_701area_enter" with "new_701area_ent". After that, click somewhere on the left side of the K-GFF window so the program recognizes that value has changed. Save file.
15. Open the file EXP_701kor.git in K-GFF.
16. Open the file 701kor.git in another instance of K-GFF (so you should have two K-GFF:s open right now).
17. Find the "PlaceableList" from EXP_701kor.git. In the end of it, there should be 4 structs whose TemplateResRef is "plc_doorinvblk". Copy them from EXP_701kor.git to 701kor.git's PlaceableList. (You can't copy more than one struct at time, so you have to copy them one by one. Make sure that you copy all 4, and not copy any of them more than once. You can click the "-" icon to minimize the struct you have copied, so you don't accidentally copy it again.)
18. Find the "TriggerList" from EXP_701kor.git. In the end of it, there should be a struct whose Tag is "To_740". Copy it from EXP_701kor.git to 701kor.git's TriggerList.
The localized string that shows when you approach the point doesn't copy when copying the rest of the struct, so it does need to be copied separately. I don't have a screenshot of that, sorry - but it works perfectly the same way: Compare the differences, click on the line you want to copy, click the "copy string" line from the quick menu, click the correct line on the 701kor.git (the one that the localized string is under of, "TransitionDestin") and click "paste string".
19. Save 701kor.git and quit both K-GFF:s.
20. Open 701kor.mod in ErfEdit and add resources 701kor.are, 701kor.git, new_701area_ent.ncs, to_740.utt and wp_valpath.utw in it. Replace as needed. Save file, quit ErfEdit.
21. Put the 701kor.mod into your game's Modules folder overwriting the one that is in there (it should be the one that Korriban Expansion installed, unless you did something I didn't tell you to do).
22. Launch your game, pick up a savegame from before ever visiting Korriban, and you should be good to go.
That should do it. If it doesn't work right, please let me know. I may have forgotten something, I still have a terrible headache.
Known issues you should be aware of
These seem to be issues with the Korriban Expansion itself, so I won't touch them in this compatibility patch.
The quest "Great Escape" is empty.
Kreia's level is reset during the mission, so she is like she is first when she joins your party (influence, however, remains). Her equipped items potentially may disappear also, so it might be a good idea to remove them before proceeding the quest.