Now here's my question: can I requeue for the same LFRs that drop the Titan Runestones and get those, too? Or is that, once I've gotten the Secrets off the last few bosses of ToT, I can't get them again?
You can not get them unless they changed it in patch 5.4. When I did it a couple months ago you could not kill the bosses again and get Runestones off them in the same week you killed them and got Secrets.
you can get runestones from SOO lfr as well.
also after you finish runestones you need to get an item off lei-shin, you can do him twice and get the item the second time.