What you suggest I have done many times and is on the right track. Check sites like Lightolier and Halo for ideas and examples. Go to their recessed lighting sections.

Thank you for the reply. The hallway is narrow with 8’ ceilings so a pendant light is a bit intrusive, which is why I’m looking for flush or semi-flush. I’ve searched: “Shadow casting ceiling lights” “Shadow play lights” “Flush light , shadow patterns” A combo of this.

It's interesting how different things hit people so...differently. I too have a visceral hatred for light fixtures which cast shadows like that. I can't even begin to explain how much I hate it, nor even why I hate it. I just do. However I will be the first to admit that I can be a loon. LOL. So if you like the patterns in those shadows I wish you good look on your search. I can tell you that there are about eleventy-million light fixtures available which are unsuitable for use in my home, so you have a lot to choose from. Again, LOL....

Lighting is big issue in any design . The light in the hall will always cast shadows there is no way to avoid that without getting new lighting . All lighting needs to be layered to fill those shadows. I am a bit confused as to the style since you seem to not have a real choice of style. Your front door says Victorian your furniture says modern and the lights I see are very traditional. So maybe tell us what you want to go with style wise. If modern is the choice get rid of the fan with light to start . All those pot lights in thta sloped ceing are pretty useless Start by addinfg lighting on end tables on the soaf in thta large space where there is no TV some great art on that huge wall in sloped ceoings I often do some cable lighting to get light where it does some good . I must be blind I see no fixtures in either of the living spaces other than pot lights . You need floor lamps, table lamps and chandeliers hug at the proper height bit I need to know what style you want.This is cable lighting I use Tech the real good part is the fact you can get light at the more human height and into spaces where lamps can be hard to add . Tech has many different heads I have even used the cable to get drop fixtures over end tables.