Basis conjecture for hybrid Grothendieck polynomials

Let $\Lambda=\bigoplus_{\lambda}\mathbb{Q}(\alpha,\beta)s_{\lambda}(\mathbf{x})$ be the ring of symmetric functions over the field of rational functions in $\alpha$ and $\beta$, and let $\hat\Lambda$ be its completion consisting of formal power series in Schur functions, possibly with unbounded degree. For each partition $\lambda$, let ${G}_{\lambda}(\mathbf{x};\alpha;\beta)$ denote the hybrid Grothendieck polynomial of shape $\lambda$. Basis conjecture. The family of hybrid Grothendieck polynomials

$$\left\{{G}_{\lambda}(\mathbf{x};\alpha;\beta)\right\}_{\lambda}$$

constitutes a basis of $\hat\Lambda$. Stable and dual stable Grothendieck polynomials are already known to form bases of $\hat\Lambda$; the conjecture asks for the analogous basis property for the two-parameter hybrid family.