I saw from other posters to try an automatic feeder and a treat ball. I think the treat ball may hold her attention. So from what I understand, everyone thinks she is bored??? If so, do you think she is wailing and meowing all day when we are at work?
I'm sorry that you've been having such a tough time with kitty waking you up so early.
I couldn't say for sure, not having met your cat, but cats don't tend to do a lot of meowing when their humans aren't around. Cats don't really need to meow to communicate with other cats, prefering body language or more subtle vocalizations like chirps and trills. Meowing is primarily a means of communicating with people--who're a bit slow on the uptake. So, most cats don't do much meowing when they know no one's home.
One of my previous kitties did meow quite loudly sometimes when everyone else would leave if I was upstairs behind a closed door. I don't know if he was searching for me or wasn't sure if he was alone and was trying to attract the attention of anyone who might still be around, but it was a very distinctive meow that he would only do in that situation. It was sort of a two part meow with a lower meow followed by a higher -ow, which gave it a questioning tone; amusingly enough, it sounded phonetically like "Hel-lo?" He only did it for a short time after people left and it wasn't constant, then he would go find somewhere to sleep.
Keeping in mind that cats are naturally more active at night, it is likely, considering how much cats sleep (around 16 hours a day!), that, with you and your husband away during the day, Katty is spending much of that time sleeping. If she's slept all day, it might be quite natural for her to feel alert when she wakes up at 4am.
You said that Katty picked up the behaviour about a month ago. Did anything change that might have precipitated the meowing, such as your routine or Katty's environment?
The most important clue to solving the problem seems to me to be determining why Katty's meowing, as that will affect what steps you'll need to take to stop the behaviour. Do you get a sense of what she wants when she meows in the early morning? Does she try and lead you to her food bowl, for instance, when you get up to try and get her to be quiet, or does she act as if she wants to play?