I don't believe 3 consecutive axes intersecting at a point rules out closed form solutions. Although i don't have a reference for this.
You should investigate OpenRave and ikfast. This will generate library independent optimized C++ code with closed form solutions for a wide variety of kinematic chains and IK types.
I found this paper that might be of interest to you:
Luo, R.C.; Tsung-Wei Lin; Yun-Hsuan Tsai, "Analytical inverse kinematic solution for modularized 7-DoF redundant manipulators with offsets at shoulder and wrist," in Intelligent Robots and Systems (IROS 2014), 2014 IEEE/RSJ International Conference on , vol., no., pp.516-521, 14-18 Sept. 2014
While it describes a 7 DOF arm, its shoulder and wrist joints don't intersect at a point. You might gain some insight from their formulation, or perhaps some of their references.