I have rescued some baby joggers from the trash over the years. The wheels have an axle sticking out one side of the hub, which you stick into a tube on the stroller, and then there's a spring to hold them on. They're easy to pop on and off. I suggest you find a couple those wheels and find a tube of the right size. 1/2" copper plumbing pipe is the right size, and I'm sure that's not the only option. Anyway, mount the tube permanently to your 'cello case, and pop the wheels on when needed. You will need to figure out how to keep the wheels from popping off when they shouldn't, but that shouldn't be hard. A set screw, for example, would do nicely.

but the wrong metal, it's rather soft, so won't be reliable..

I'd think a set of cradles to carry the case , somewhat like
kayak carrying, on car, roof racks. is another approach,.

I have the Burley Travoy trailer and I think it would fit your needs nicely. It really is a a well thought out trailer. I use it to carry two camping chairs and picinic lunches for my girlfriend and I. I used it to carry home a big toolbox that I found on sale and today I will use it to carry a suitcase that I bought which is sitting at work. Plus I use it to go grocery shopping as it as like a bundle buggy when in the store. It folds up to nothing when not in use. One of the things a like about it is, the ease in which I can take my bike and trailer out of my unit, into the elevator without having to take a two trips which I had to do when I had the Chariot and Yak trailers. Those were great trailers but didn't suit my needs all that well. The Burley does.

Thanks for all the replies. I have an REI close by so I can "buy" a burley travoy and if it doesn't fit, I can return it within 30 days for a full refund. I'll give that a shot, and use my standard bike on the bus, which rarely has a full rack.

Rhm and fietsbob, thanks for your suggestions, too! I think it would be a great, eventual, project to design a trailer, where the frame would basically be an air-travel case with wheels, such as the baby stroller's attached. I could use a gig bag then to put inside the travel case and it'll be nice and insulated and cushioned from shock.

Do you think the burley travoy could fit inside a backpack or messenger bag? Not necessary but I already am carrying a lot of stuff