I think that your ultimate problem is that she eventually gets what she wants. Yes, some of it is attention seeking, but she is also learning a tremendous lesson in control right now, and if you think she's not learning self-control, you're wrong. What she had learned, is that if she screams and irritates you for as long as she has to, EVEN throwing fits in time out....she WILL eventually get what she wants, and she's exercising as much control to throw those fits as she needs to. Here is what I would suggest: do NOT give her what she wants when she acts like that...period. If she starts whining for food, tell her you will not give her anything until she starts asking nicely. If she won't, don't give it to her, eventually she'll get hungry and behave...and no, she won't starve. Also, tell her, that if she doesn't stop right away, that when she DOES get food, it will not be what she wants. Either she can behave immediately and get what she wants when you can get it for her (for example, if you're feeding the baby), or if she doesn't, she will eventually be able to eat, but it will be what YOU choose. Say she wants cereal...if she doesn't behave, give her breakfast, but make it toast instead, and tell her she can try for cereal again tomorrow and that she needs to remember this. If she starts up the next day asking for cereal and looks like she might start a fit, remind her gently, "I will get you cereal when I am done feeding the baby. Do you remember yesterday when I gave you toast because you threw a fit? Don't make that happen again." Do that for everything...games, food, toys, stories. When she does behave, then reward her with what she asks for, but only if she does it the first time....don't let her throw a fit for 10 minutes, then ask nicely, then get what she wants. Keep reminding her that she needs to ask nicely the FIRST time, and if she does, then she'll see nice results.
If she's throwing a fit, and time-out on the stairs isn't working, and if you don't believe in spanking at that point, put her in her room. At this point, it doesn't matter if she plays with toys, what matters is that you teach her that if she misbehaves, you will pay enough attention to her to send her away from you....and that is ALL. When she is willing to behave, she can come back down. If she screams so hard your husband still cannot talk to clients, that's when the hammer needs to come down, because that is unacceptable, and you need to be the adult and win the argument.
I know this may sound like a really harsh attitude, but at her age, she CAN contol herself, and you need to be serious if you seriously want her behavior to change. It may take a little bit, but I think that you will be surprised at how quickly her behavior will adjust if she sees continuity from you on this issue. Best of luck to you!!!