If she is like my little monster, ANY progress in destroying the barrier
will encourage her to keep going.  I too was unable to train my Eris to
stop digging and jumping at the barrier.  But I learned that if she feels
that getting over/under is 100% hopeless, she should give up.
 
I would suggest not using cardboard.  Go to Home Depot or a similar store
and get some fiberboard.  It's like cardboard on steroids--tough enough
to stand up to ferret claws but easy to work with.  You can also use
nuts, bolts and washers to build simple shapes with it.  For example, I
have used it to block the ferret pathway at the back of my bookshelves
and that kind of thing.  I also made a removable hallway barrier out
of it (with a split PVC pipe at the top--they can't get a hold on the
curved surface and pull themselves over).
 
Anyway, it comes in a 2' x 4' piece for about $4, if I remember right.
Cut it to the size of the gate, drill some holes in it and use zipties to
secure it to the baby gate.  Then you can use the leftover material and
some L brackets and screws to make a sturdy replacement for the
hinge-blocking cardboard.
 
As for the carpet, I am not sure what to do.  Perhaps you can make an
"L" shape on the bottom of the barrier... a few inches of fiberboard
protruding from the bottom of the barrier... a few L brackets and some
nuts & bolts would be all you need to make it.
 
Personally, I gave up and let Eris tear up the carpet since I am planning
on pulling it all out and putting a hard floor in the ferret room anyway.
 
Anyway, good luck, and check out the fiberboard.  It's cheap and easy
enough to work with that even I can make ferret blockers.
[Posted in FML issue 4568]