Papier mache moose horns

This is how the papier mache horns turned out.  I guess they'd need a few more layers of paper, so they might be a bit bulkier on the finished moose.  

There is a problem with stability.  I think I'll need to weight his back legs to improve his balance, but the horns themselves also keep falling forwards/backwards - they are not very well anchored.  I have tried stitching around the wire frame, but it doesn't really work.  

With this moose, the wire simply goes across the top of the head and up into the horns.  The alternative would be to take it right down into his body, so I can pack stuffing around it and hold it more firmly in place.  The disadvantage of this is that, because I'm using quite heavy duty wire, when I start bending the ends back and forward to get the horn shape right, it wiggles the bit in the middle, causing havoc with his stuffing.

I guess the answer is not to sew him up until the horn shape is right.  Feed the wire in, stuff around it, mould the wire into shape, then re-stuff if necessary and sew him up.