Now, theoretically speaking, if we could reproduce the differences in non-breeding and breeding diet of tropical birds, we could regulate their hormones even if they are kept at 12L/12D but not all birds are tropical or even semi-tropical, there are parrots from temperate zones, and, practically speaking, nobody can manage such a feat. I know I could not leave a parrot hungry or send him to bed without dinner and I don't know anybody who could so the only sure way we have is to make the tropical ones revert to photoperiodism and that means following the sun and exposing them to dawn and dusk (it's the change in spectrum that happens during twilight that entrains the circadian cycle which, in turn, falls into the circannual -meaning the different 'seasons' -breeding, molt, migration, etc- during the year).
Now, as to your dilemma, yes, you can keep a parrot in a human living area and still keep them to a solar schedule. I have birds in my living room (cardinals) and in my dining room (Senegal and redbellied at this point in time), I turn off the overhead lights when the sun is setting (this time of the year at 6pm), feed them dinner and, when night falls and they are already half-asleep on their roosting perches, I cover their cages - in the morning (I get up at 5:45 am this time of the year), I uncover their cages and turn on the overhead lights when the sun is out on the sky (7 am this time of the year). But this means no diner parties, no company on evenings or nights, no TV, no radio and pretty much keeping noise to a minimum (we even whisper) -and the reason why my husband is willing to spend thousands of dollars in two and not one new birdroom in the attic
He dreams of the day when all the birds are upstairs and he can get a BIG TV set in the living room to watch his soccer games at night (he is not been deprived, mind you, he has a pretty big one right now in his study where he watches his games from a nice recliner). There is a couple I know who puts the sleeping cages in their dining room, turns off the lights, feeds them dinner and, when the birds are asleep, they cover the cages and turn on a single end table lamp in the living room where they have the TV very low and, right before they go to sleep, they turn off the light and TV and uncover the cages so the birds get the benefit of dawn the following morning. And, I know a lady who lives in a studio in Manhattan that has a blackout curtain from the ceiling to the floor separating the area where the birds cages are so she can watch TV (low volume) and work in her computer after night falls. And I can personally attest that both these systems work because I see these birds periodically and they are all in perfect tune with the seasons.Now, your idea of putting a sleeping cage in the basement would be OK as long as you have a basement that has enough natural light coming in so the bird can be exposed to twilight. Mine doesn't but my ex-husband has his family room in the basement and this part of it has a door and a large window to the backyard because the terrain there is lower than the front and allows for it so, if yours is like that or you have good windows, you should have no problem.
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