I've never used the Hazelbaker. Are you inserting the tube before or after the baby latches? If you're doing it before, that may be part of the positioning problem. It's not super easy either way, though.
The Lact-Aid is a bit more like a straw- you have to suck it up. There are still some problems wiht leaking, but it's not as bad There can also be problems with leaks when you're breastfeeding without a supplementer and bottle feeding, nature of the beast.
The Lact-Aid has two size bags: 4 oz and 8 oz. I've seen people say that a BF'd baby should never be given more than 4 oz at a time because that's all they get from the breast, but I don't know if that's true or not. With as long as your baby's feeds are, I'm not sure how much it would help to use the larger bag.
Are you using formula or breastmilk? That makes a big difference, especially for nursing in public. Formula has a much shorter shelf life, it's only good for an hour or two at room temperature while breastmilk is good for a few hours (unless it's really hot). I've seen someone suggest those tops that have a bra-shelf built in, you put the bag in the bra-shelf and then you can NIP without being obvious. If you want, you can also try to get your baby used to a cover- you're call on that, though, especially in the summer. You can place the bag in cold and let your body temperature warm it up. That'll work with either formula or breastmilk but, again, formula has a shorter shelf-life so you'll need to be relatively sure that your baby will want to feed quickly, especially given how long he feeds.
For traveling: Eurgh, that sounds awful. We did a 20 hour stint (8 hours on a plane, long layover, then 1 hour) and it was murder. Again- formula or breastmilk?
Either way- look up the policies. Print them out. You're allowed to bring way more liquid than others, and you can bring it in a cooler. If you're using breastmilk, you'll have to bring as much as you'll need (I advise extra) for the trip. Formula actually may be easier here because you don't need to keep the RTF cool the way you do breastmilk.
Warn them that what's going through the x-ray machine is a breastpump and be prepared for some more extensive screening. Electric pumps look very suspicious with all the wires they have and such.
You can place the used supplementer (and pump) in the cooler until you get off the flight. It's not perfect, but you do *not* want to be washing them in the airplane toilet.
I don't have advice on pumping on an airplane but it can and has been done. Again, look up your airline's policy, print it out, and have it readily available in case a flight attendant wants to give you crap. A nursing cover isn't a bad idea, you can pump under it while in your seat, especially on overnight ones. Are you traveling with a partner or will you be juggling an infant and a pump?
I've heard it gets a LOT easier as the baby gets more body control, especially head, and can position themself more readily. That won't be long now. The first 6 weeks are the worst no matter how you're breastfeeding.
this is just a moment in time, step aside and let it happen