Is it the kind of spinning where you turn a form and use a "big spinny thing" to spin/roll a disc of aluminium over the form?
I used one at a college years ago, we made up cup and vase shaped containers, funky shapes with integral bases. Can't remember the name of the machine though.
Was a big contraption though quite simple. Haven't seen one in any of the other colleges since or at uni.
Does the design really call for it? Could one off's maybe be made by hand?
There are folk with pole lathes who could make hardwood forms. You'd have to wait for them to dry but then you could beat sheet round them then cut & weld a seam.
I've got access to a tig set but have never worked with aluminium as light as you're thinking of(in fact I've hardly worked with aluminium at all, only practice pieces about 7mm wall thickness).