By "eye box", do you mean the spot you have to hold your eye in to view through the scope, or the edge to edge field of vision through the scope? To fix the former, look for a scope with a larger exit pupil at max magnification. To fix a limited field of view, the easiest fix is to use a scope with less magnification. For shooting within 500 yards, I'd suggest something like a 2.5-10X or 3-9X magnification range.
The SWFA SS 3-9X42 FFP is only slightly above your budget, as well as the Vortex Viper PST 2.5-10X44.
U.S. Navy (Retired) 1994-2015