Well, basically after messing around for about a week and spending countless hours I can tell you for me the 300 Expansion does nothing but cause issues.  For example, with just the main aircraft installed I never have any CTD issues.  With the Expansion installed I have crashes when ever I reload FSX after a flight in the 300.  Every time guaranteed.  It also crashes FSX sometimes right after a flight in the 300, as I'm trying to close FSX.  There are also other minor issues that just make this already beautiful yet finicky airplane a pain in the &@($* when the Expansion is installed.  So for me I DONT use the expansion and all is well, but I would really like to see the bugs worked out so I can use it.  It just feels like it was thrown together and not really tested before release.  The plane is wonderful though and my favorite small aircraft, however it could be a lot better with the Expansion bugs worked out.  Crash.

I have 2 versions for this plane: one with the Navigraph Extension and another with the GTN750 mod.
 
Probably can't help much as I run P3D v3.2 and have the expansion working just fine.
 
What Windows version are you using?
Where is Your FSX installed?
Are you able to post a crash report?

Things I would try:
1. Make sure the Expansion Setup EXE is not marked as blocked in properties. (General -> Security)
2. Run the Navigraph Expansion Setup as Administrator (right click on it and select Run as Administrator)
3. Run FSX as Administrator. (same as above)

I run FSX/Accel, windows 7 64bit.  I checked in the CarenadoNavigragh and the "cycle" is updated properly.  Their were 2 install versions, 1 for mac I assume and the other for Normal.  I used the Normal. Flights work well, its just after a flight when I shut down FSX,  when I retsart it and chose the 300 again it crashes it guaranteed.  Usually it will load fine the "next" time FSX is loaded, after a crash.  Without the expac, I can retsart FSX all day always re-choosing the 300 and never a crash.  I've reinstalled everything a 100 times and its the same thing everytime.   I always start FSX, ASN ect... as admin and my Navigragh is always "active" and updates and runs just fine.  I chose "mapping" it it finds "all carenado products" and then updates.  When I start FSX it always loads the new cycle but only for that 1 time as it was designed to.  Everything works fine, its just the crashes.