Consistency of separating generalized null additivity from partial-slalom additivity

Let $\kappa$ be the cardinal in the generalized slalom setting. Write $\operatorname{add}(\mathbb Q_\kappa)$ for the additivity of the generalized null ideal and $\operatorname{add}^{\operatorname{partial}}(\kappa)$ for the additivity characteristic defined using partial slaloms. For $h\in\kappa^\kappa$, write $\operatorname{add}(h\operatorname{-slalom})$ for the additivity associated with total $h$-slaloms.

Partial-slalom separation conjecture.

$$\operatorname{CON}\bigl(\operatorname{add}(\mathbb Q_\kappa)>\operatorname{add}^{\operatorname{partial}}(\kappa)\bigr).$$

In particular,

$$\operatorname{CON}\bigl((\forall h\in\kappa^\kappa)\ \operatorname{add}(\mathbb Q_\kappa)>\operatorname{add}(h\operatorname{-slalom})\bigr).$$

Moreover, the assertion that some total-slalom characteristic always agrees with generalized null additivity is not a theorem of ZFC:

$$(\exists h\in\kappa^\kappa)\ \operatorname{add}(\mathbb Q_\kappa)=\operatorname{add}(h\operatorname{-slalom})$$

is not a ZFC theorem. These claims refine the preceding observation that the partial-slalom answer is negative and formulate the desired separation for total slaloms. The supplied text gives no resolution.