Existence of a universal strict formal group over a ring

Let $K$ be a $p$-adic field. A universal strict ${\mathcal O}_K^\triangleright$-formal group means a strict ${\mathcal O}_K^\triangleright$-formal group with the universal property developed in the preceding results, defined over a ring $S$.

Universal strict formal-group conjecture. There exists a universal strict ${\mathcal O}_K^\triangleright$-formal group over some ring $S$.

Such an object would complete the preceding construction of strict ${\mathcal O}^\triangleright$-formal groups and provide a universal parameter space for them. The source presents this as a tempting conjecture and notes that it may be difficult to prove; no resolution is given.