I'm the last one to offer advice really, as I struggle with some fairly basic things myself sometimes, but I maintain you have no choice but to first remove the handles etc, and then remove the door card. Whatever the problem is, (presumably it's the cable that runs to the outside handle), you're gonna need full access to even assess what's wrong. Sorry.
I put up with the same problem for 3 years! I found lubricating the outside handle mechanism with a spray of WD40 helped. My door cards were rather fragile and I never wanted to take them off as I knew they would n't go back on and I'd have to buy new ones, therefore I never wanted to investigate the root of the problem.
I just got in the habit of pushing the inner handle back in place each time
my 1750 gtv had a similar problem, it would open from the inside but not the outside. i'm not sure if the latch is the same.
the latch worked by rotating a little catch on the door. the catch would rotate to release the body of the car. when the inner door lever was pulled the latch would rotate, however when the outer door lever was pulled it did not rotate as much so the latch wouldnt completely release. if you cannot close the door until you pull the inner handle perhaps the latch has rotated down over time. you may be able to rotate the latch housing in the door. so that the inital possition of the latch is higher. for my car the problem was the door hinges had worn down and the door was sitting low. i could open it from outside when i lifted the door.
so check the if u can lift it and get it to open or rotate the latch housing. its probably something to do with the latch not lifting high enough. i hope thats relevant to your door mechanism.