Hi @reporting - You mentioned that you are using Service Provider (SP) initiated SSO, which is the right way to do this since then, QuickSight knows which SSO service you are using and your users can visit a QuickSight URL that has the account name (aka directory alias) in it, and QS will redirect your user to the SSO page. I think your point is that your users may not know the name of your quicksight account, which I understand is a realistic situation though is a bit harder to deal with.
It looks like you discovered that you can add the account name into the URL manually (by adding “&directory_alias=blah” to the end of the URL), and this is automatically added to URLs contained in links you find in an emailed report or the notification you receive that a dashboard has been shared with you for instance, but does not get automatically built into the URL you see in your browser when on a dashboard page if someone were to just copy/paste it.
Vanity/custom domains for your specific QS account are in consideration by the product team, though I dont have an ETA to share with you.
Aside from user education as well as hoping the user will know they could also access QS via your SSO portal and then opening the dashboard link again, we would need to implement one of your two suggestions, which are both spot on.