Yeah, well what I ended up doing is just throwing Freudenstein's eqn into Mathematica, have it solve it for θ5 and then just use that... it wasn't a pretty equation, but it seemed to have gotten the job done:
y = -cos^(-1)((160 cos^2(x)-582 cos(x)-2 sqrt(9216 sin^4(x)+49319 sin^2(x)+2816...