I flew from San Jose, California to Newark, NJ with a bird. I also got the airline approved carrier and put some seeds and an orange (instead of water) in it but what I did was get a flight that made 2 stops of 1 or 2 hours and, during the wait to board and the stopovers, I went into the bathroom and let her out of her carrier so she could drink water, poop and hang out with me in private. I was lucky that none of my flights was unreasonably delayed so everything worked out just fine BUT it was a one time thing as I would not consider flying regularly with a bird (way too stressful).
As to boarding... well, I tell you, I would never do it. Not to any of my animals. I have heard horror stories about these places - my cousin's dog had to be euthanized a couple of years ago because of the boarding place's negligence in noting the dog was sick so he went from a respiratory infection to pneumonia! And she swore by this place because she had used it many times in the past and had all the bells and whistles. No place is good per se, it's the current employees that make the difference and, as those places don't pay their peons much, who you end up getting to take care of your animal is a gamble I am not willing to take. I would leave them with somebody instead. An important wedding anniversary is coming up for my husband and I and, as we haven't been able to take more than two days together anywhere in the last 15 years (precisely because of the animals), I have been looking and looking for a solution and finally found a neighbor who is willing to move into my house and take care of all of them (I am paying , of course!) while we are out. It's not the best solution because animals don't like to be cared for by strangers but all my animals know him (he has done work in the house several times, the last time replacing the floor in the birdroom so even those birds know him already) and they are staying in their familiar place and keeping their known routine. Is there any chance that you could get somebody the bird already knows to come to your place?