The countable-union conjecture for well-quasi-orders

Let $P$ be a well-quasi-ordered poset. A better quasi-order is a poset $P$ such that the quasi-order of countable sequences from $P$ under one-to-one domination is a well-quasi-order. A poset is a countable union of better quasi-orders if it is the union of countably many subsets, each carrying a better-quasi-order induced from $P$.

Countable-union conjecture. Every well-quasi-ordered poset is a countable union of better quasi-orders.

This conjecture was proposed in work of Abraham, Bonnet, and Kubis. The supplied text gives no resolution status, so whether every well-quasi-order admits such a decomposition remains open.