Jump menu - display current path as the default option for multiple arguments

When creating Jump menu, this is an option I have:

Select the current contextual filter value
If checked, the current path will be displayed as the default option in the jump menu, if applicable.

Works perfectly. However, only as long as the the path has only one argument (the one that defines the default option).

What I was hoping to do is to chain two (or more) Jump menus to narrow down list of options across several node types that are referenced to each other. I do this using Panels.

It all works fine, the jump menus are being added as I drill through the node references, and the right rows are being selected, and the appropriate arguments are being added to the path.

The problem is that as soon as I append another argument, the Jump menu one level up turns into "- Choose - ". Instead of keeping its selected value.

From a user point of view, it would be great if they could see the previous choice they have made.

Anybody any idea if it is even possible? Any advice very appreciated.