Hello,
I've had the some troubles with my Matt Freeman and had to extract entire truss rod. Unfortunately, the "brown insert" is not plastic it is a piece of walnut. So ironing it out will probably not work. Also hex key is 5 mm, not 4. I've heard torx keys sometimes help as well. But in any case you WILL need to remove the insert...
If you have tools, courage and correctly installed hands you may try to drill the insert out as I did. Just get the long drill:
View attachment 2814730
When you get your problem solved you will may want to reverse the drilling. I was lazy and just used black tape. But now I have access to the nut if I need
View attachment 2814754
It is not too hard to do just take care of neck's finish - scratches are hard to remove. So protect it with masking tape or other kind of protection. I've put the plastic bag (mangan strings

) on the headstock while drilling