Aimee Blessed Momma to 4 amazing boys, P ~ 9 H ~ 7 J ~ 4 and B ~ 1. Happily married to D Living my almost dream life on an urban homestead, hoping for our forever land to find us soon!
Now, I have a much calmer buck. My does used to like to squeeze through stuff, too, but my current does (a larger breed) aren't as sneaky that way. So we do OK with 4' wire fencing.
I'd agree that two strands, one on top and one lower, standing out from the existing fence, should do OK. Good luck. We had a rough go when our animals weren't securely fenced, and I understand the anxiousness. Panels are effective, too, but they need to be really well secured.
The kids are a bit more tricky when they are younger, so we keep them in an area consisting of 4 cattle panels and then train them to the fence when they are a bit older.
Trying to build up my house, not tear it down . Got 3 wonderful kids , blessed with a wonderful husband and have the privilege of staying home full time to enjoy it all!