For the round rods, one idea is to get a mini-lathe and then engineer some sort of ultra-thin cutter. It's likely just as much material loss as a bandsaw, but much more accurate.

The Little Machine Shop had the highest quality mini-lathes back when I was researching. This model is a true variable speed using a brushless DC motor (50-2500rpm):
https://littlemachineshop.com/produc...ory=1271799306

If you have square stock, you could engineer a saw cutter blade that mounted in the spindle jaws and then mount your stock on the radial arm. This would allow an ultra precise cut.