what you can do is print in a wax like material and make the rings from actual metal in a 'lost wax/plastic' process. That's your best bet for a 'printed' metal ring.

Same kind of thing as far as the statues go. Print a plastic statue and make a silicon mould from it that you can use resin in.
Or print a flexibe plastic mould directly.
That's pretty simple to do.

So while you can't use those materials direct for your models, 3d printing can help make them easier to make.

Sounds like a delta could be your best bet. They tend towards taller prints than cartesian machines.
They are also much easier to build.