Climbing techique with panniers and cleats
One thing that may help a lot is shifting some load weight forwards.  In other situations I've found that a surprisingly small amount of weight shifted from behind the back axle to the front forks improves handling a lot.  For example rather than mounting a D lock behind a child seat, I put it on the front forks. That's something like 1% of the total weight, or 4% of the non-rider weight.  

This may lead to a bar bag, bar/fork-mounted bottle holders, or front panniers, though I'm trying to avoid the latter (as it seems are you).

Even loading differently within the panniers might make a difference.