I don't think K-homology will satisfy your requirements. The reason people think of G-theory as dual to K-theory is because for proper $X$, the graded space $Ext^*(F,Q)$ is finite-dimensional for $F$ a flat and $Q$ a coherent sheaf, and this defines a pairing. There is no such finite-dimensionality even for pairs of topological vector bundles over a topological manifold. In particular, there is no reason to expect there to be any sort of interesting map $KU^*(X)\to KU_{-*}(X)$ for non-smooth $X$. 

Your #3 is interesting and would probably satisfy all your requirements, although I'm not sure how well functoriality of Blanc's construction works with respect to functors without any finiteness conditions (it most likely does). A simpler alternative might be as follows. Take some topological Abelian subcategory $\mathcal{C}$ of topological sheaves of modules over $C^\infty(X)$ which is stable under extensions and tensor products with bundles and which contains all coherent sheaves (extended to $C^\infty(X)$). One possibility is to model the theory of constructible sheaves and take sheaves which are repeated extensions of pushforwards of (analytic) bundles on algebraic subvarieties. Now take its topological Waldhausen K theory, and invert $u\in K_{Wald}^2(\mathbb{R}-mod)$ (which acts on the topological Waldhausen K-theory of any $\mathbb{R}$-linear category in an obvious way). If you had started with just the category of line bundles, you would get $KU^*(X)$. Here you will get some new theory which will satisfy your requirements.