Lighting a large space when you can't use table lamps.

Have you considered torchieres (spg?) , floor lamps or small canister lights that shine up behind chairs or large potted plants?

Just hide the cord.

there are anti trip put on the floor run the cords on the under side thingies, had them in house 2 when i needed to run a cord across a doorway. the cords were tucked up in, and didn't hit the floor.

Would hanging lamps work?

How about a chandlier in a corner seating area that has a long chain with a plug or it can be added to it and hook it to the ceiling with s hook, like a swing chandlier. There are tracks that can go along the wall or floor to hide a long extension cord to bring electricity to the area you need it for and it can be painted to match the wall or molding. Spot lighting in corner I guess they call them can lights. Track lighting on ceiling with those track covers for the cords. Ask Home Depot and lowes you can point you in the right direction and give you more ideas.

I assume that there are outlets on the walls. Put up a hanging light and cover the cord with the cord covers you can get at the home improvement stores.

arching floor lamps, with multiple lamps. Put it behind the couch or on the wall furthest from the window to help balance light in the room.

can you add recessed lighting or is it not allowed

Rope Lighting that plugs into a Socket? or Individual press lights (Battery)?