I have the Tamrac Velocity 7 sling pack. This is what I carry in it... Alpha 100, KM 70-210, Tamron 28-75 and either a flash or KM 50mm lens, without any problem. Most of the time I don't carry across my back just out of preference but just on my right shoulder. I have the Lowepro Slingshot 200 basically for storing my camera gear but do use it on occassion at the parks. Hope this helps.
Thanks to everyone for the suggestions.

Today we went to a local festival, and I took the A350 with me, in the old camcorder case (shoulder bag) I've been using since I got the camera. After using that crappy bag all day, my back was
killing me...and I was only carrying the camera and my Tamron 28-300mm lens. This convinced me that I would probably be better off with a backpack or a sling bag, rather than the shoulder bag I was previously favoring.
So, on the way home we stopped at
Best Buy. They had the Lowepro Slingshot 100, which was a perfect fit with some room to spare. But, I think it would be better suited to a taller person than myself. I'm 5'5", and it just didn't sit on my back right, no matter how I adjusted the strap. Also, I'm a woman, and the strap was crossing my chest in an uncomfortable manner.

However, I did really like how it had a separate top compartment, where I could have carried miscellaneous stuff. The waterproof cover was also a very nice feature.
From there, we headed over the the mall, to Ritz Camera. They had both of the bags I mentioned in my original post. I really liked the looks of the Tamrac Express 6 (the khaki colored one doesn't look like a camera bag at all), but it was just a bit tight from front to back. The 7 would have probably been perfect, but the store didn't have it. However, after carrying a shoulder bag all day at the festival, I was pretty sure I didn't want to go with that option.
They also had the Tamrac Velocity 6 & 7 sling bags. The 6 was just a bit too small. The 7 however, was perfect for my needs, and that's what I ended up getting. Unlike the Lowepro Slingshot 100, this one sits on my back quite comfortably. It doesn't have the separate top compartment for my miscellaneous junk, but I can live without that.
I'm very glad that I bought one "in person", rather than buying online. I would have saved $10 by getting it at Amazon, but being able to try it out in the store was nice.
And of course, I didn't get out of there without buying other stuff.

I bought a comfy neoprene neck strap, since the one that came with the camera turned out to be very uncomfortable. I also bought a Lens Pen. Now, I just need to buy a couple of filters to protect my lenses, and I'll be set...for awhile anyway.
Forget picking a bag to carry all day! Just carry the camera itself, on a comfortable strap of some kind, and leave the bag in your room.
The only thing a camera can take pics of when it's in a bag is the inside of the bag. And while the inside of a camera bag may be a fine place, I have no burning desire to start a collection of pics of them. But I do have a burning desire to take pics of my vacation experiences, which is why my camera stays out and ready at all times when I'm touring - turned on, lense hood in place, lens cap off. I do have it set to go into sleep mode after about 3 minutes, to save battery power.
Your 28-300 lens is an excellent walkaround lens for the parks. And since the only other lens you have is a kit lens anyway, you won't need a camera bag to lug around with spare lenses (I use a Sigma 18-125 as my walkaround lens). You will need a spare battery and some spare memory cards, but these are small items that you can easily fit in your pockets or a small waist bag, rather than lug around a huge camera bag. I even carry a pocket-size tripod for those night shots when I need stability - it works great on tables, trash cans, railings - but I carry it in a belt holster and not in a bag.
So get yourself a nice bag for travelling that will protect your gear through airports and on planes, but don't look for something to carry in the parks.
Go bagless.
Thanks for the advice Will. I did consider not using a bag in the parks, but I do all of the rides. I'm a bit scared about knocking the camera around while on a ride. Rain also makes me nervous, although I suppose a large zip-lock bag would work in a pinch.
I did buy a comfy neoprene neck strap today, and I'll probably end up carrying the camera like that most of the time. But, I like the security of having a bag to put the camera in some of the time.
Oh, and I did really like the 28-300mm lens today. I hadn't used it outside yet. I was able to get a lot of up close shots, that the kit lens wouldn't have done. However, the lens is crappy indoors though...I definitely need good light for it.