I think that definitely looks better!
At the risk of over-cluttering the page, you might even add “only used for quoting indirect sources” somewhere on there. With that explanation, I think it becomes pretty clear that we’re combining the quotational とwith the… question/uncertainty marker か here.
Also, the link to the first reading on that grammar point is broken
Would it be possible to write a script that runs daily (or every few hours) to check on the status of the linked webpages? Something like that would help you catch broken links before users do, and if you see any patterns, it might be a good indication to avoid certain sources if they’re more prone to downtime than others.
Edit: んだって can also be used to quote indirect sources, so I changed the suggestion to: “only used for quoting indirect sources” to more accurately convey that it shouldn’t be used to quote something verbatim/directly.