Thanks, but my question wasn't really which URL to use, but the way in which CB formats it.
The issue seems to be that the URL CB creates for first time login contains the uninterpreted special entity
& rather than simply
&.
While the target content loads, this breaks Joomla's menu assignments, so that the content appears without the modules that are assigned to the Itemid in the URL.
This is admittedly a bit over my head, but I note it happens only with the first time login URL, and wondered how I might create a workaround.
But perhaps I'm being overambitious.