I've posted something like this before, so forgive me if you've already read it. There are guys that do portable sandblasting and many of them can do Soda blasting. They do this on a lot of heavy machinery, like loaders, dozers etc. The advantage is, the soda won't mess up glass or chrome, and it doesn't mess with engines like sand. It only removes paint, so if you have any rust, you'll have to deal with that separately. If you call a guy and take your cruiser to him while he's set up on another job, you can probably get it done realativly cheaply. They usually have an hourly rate and you can do a lot of paint removal in an hour or two. A lot of guys that have a nice old car that just needs paint will have it done, so you might check with a local street rod/antique car club. You do need to rinse the vehicle to neutralize the soda.
Every stripper I've ever seen used was a total mess, but Aircraft Stripper was the best of the bad.
Check the Yellow Pages for sandblasters.
Good Luck
Ed