DocGlenn,
I've made several 400+ yard shots with my .30-06 NULA, no problems. It weighs 6-1/2 to 6-3/4 pounds, depending on the scope, and I haven't had any problem shooting it from a steady rest.
One of the nice things about NULA's is that the light action allows at least a medium-contour barrel while still retaining the light overall weight. The stock helps too. Consequently the balance is more forward than in most other light rifles.