I haven't had a problem with the buns munching the doors. The fit fairly flush so there's not really anywhere that they can get hold of it at floor level. You could just make sure that the weldmesh wraps around the edges - that'll prevent massive destruction!
Have just taken a couple of pictures, sorry they aren't very good, camera doesn't like focusing on close up stuff and Macro won't work.
This is the second one I did - hinges in the corner of the wendy house mean that the door sits very closely to the wall and no chance of bunny attack - but as it is on the back of the door frame it means that the outside door closes as normal
The little bit of framing at the top of the door gave me something to use a turn button with so that the door closes in two places
If your doors don't have anything like this you could always add a small piece of timber on one corner.
The hasp was attached in reverse kindathing - so that the screws attaching the top part are put through the back of the fixing, whereas normally it would be attached and then have the long flappy bit folded back over it. Sorry if I am confusing things....
On the first door I did, I put framing around the whole door and used a large metal rod/nail type thing and put it through a hole in the door and the frame. Not as secure but it works fine and we don't have any security issues as the outer door is locked when we aren't here/at night - they have access 24/7 to the run.
I am sure that wasn't much help but it may have given a lightbulb moment of you own.
Look forward to seeing your efforts!
Helen