So far, I'm with you on your ideas, but your wanting to use stainless flex hose is not going to give you what you want because the diameter is too small for a 'zon, 'too or grey's foot and when you got one assembled, I'm pretty sure it is going to be way too heavy to properly mount inside the cage.....your purple example is about 18"-20" in diameter.....something else you're going to have to contend with is the different threads used.....take a flex shower hose.....where it screws onto the pipe at the top, that's a pipe thread, but at the bottom where it would screw onto the spray head, it it a different, finer thread & the same happens with the flex hoses for kitchen sprayers.....just sitting here mentally picturing how you would mate these different pieces together, instead of a flowing circle, you would need several adapter fittings just to match different threads.....
You might want to make a fact finding trip to your favorite Home Depot, Lowes or other hardware store with a large plumbing parts department and look at and mentally or physically measure the various threaded ends and what is required to finally get the together...I think you'll be surprised & frustrated at the same time.....for your flex hoses, you can get them in 18", 20", 24", 36", 48" & 60" chrome lengths, but not sure if you can find all in a stainless finish at the same store.....these long lengths are really extensions, so you'll want to be sure to check all of the various ends & fittings you'll need to build your orbit.....I'm sitting her picturing your enterprise & without figuring specific parts, I'm thinking you'll need two extra fittings for each T connection, so you'll probably want to draw each fitting your assisting parts person will point out to you.....
Have fun.....