Let me throw another pearl at you.... in addition to getting a 34 foot trailer from the early 90's at a reasonable price (I have read of people on this very forum with brand new trailers who have had more trouble with them than I have had with my '87 model...), you NEED to be a good mechanic.
Get Livingston's book and learn it. I'm not sure why it's so expensive...must be out of print. I got if for like $20. There are newer versions of it, but this is the version I have:
Trailer Life's RV Repair and Maintenance Manual: Bob Livingston: 9780934798129: Amazon.com: Books
One KEY to making this work is that you MUST be able to do your own repairs.
Trailers are butt-simple (excuse the slang....
) They really are. They are not hard to work on. But, if you have to have every little repair done by a professional repair shop, you'll be paying $400 to fix something that you could probably do yourself for $40. No slam against RV mechanics....it's the same with auto mechanics. But you really need to be able to troubleshoot and fix stuff yourself.
One poster above mentioned a roof leak during a cold rain. How do you fix it? Easy, you clean off the roof seams and hit them with aluminum Kool Seal. You should go over the roof BEFORE you go on your trip.
But at any rate, buy this book or one just like it right now. Read up on it. Learn the systems of an RV. They are like mini versions of the one in your house; but simplified. RV plumbing is easy. RV electrics are easy. RV mechanicals are pretty easy (especially on a trailer...motorhomes are trickier as they have a real drivetrain).
I still recommend you get yourself a late 80's to early 90's 34 foot triple axle. Do some weekend trips in it. Fix what's wrong with it. Learn to work on it before you go on the grand trip. Again, it's not hard. But, if you have to pay a Pro to do repairs for you, you're probably looking at 5-10 times what it'd cost you to do it yourself.
On these silver trailers, if you get one with a decent frame (get an '86 or newer), there's not much that goes wrong with the structure. The appliances will wear out, but you can replace them.
On my own Avion, the structure was perfect (and don't be afraid to look at an Avion 34 footer....especially pre '88....they don't use rubber axles so you don't have to replace the axles....) but the appliances were wearing out. I bought it for $7200 (I did score a deal, but you can too) and put about $5K into it. I replaced the old 13,500 btu a/c with a 15,000 unit, new toilet, new Atwood water heater, new Dometic fridge, new kitchen sink (Moen home unit), six new tires, six new shocks. I've got about $12-13K in it, and probably $25K of "Sweat Equity", but now I've got a rig that I can pull anywhere, anytime, and have no worries about it at all. I know how to fix just about everything on it. I knew nothing before I got into it....it's not hard. You just need to read. These forums will teach you a bunch. Combine that with the book and you can learn all you need to know.
I've had less trouble with my '87 than I see some poor folks on here having with brand new ones. Personally, I wouldn't consider a new one just because of the depreciation hit....though they sure look pretty.
But anyway, if you can fix whatever breaks, you are Light Years ahead on the finances.
Read up on here about "Torsion Axles". At about 20 years old, most Airstreams are going to need new axles. That isn't cheap. But you need to look at the individual trailer.
The advice of a big 5er isn't bad either. But if you have the Silver Addiction, you could also look at Avion, Silver Streak, and Streamline.
Anyway, I think you have a cool idea. I wish you the best!