The way to do it would be to print on an ultra smooth paper or other surface, then coat it with multiple layers of high-gloss varnish. You won't get the gloss without a varnish coat. But, due to the wide gamut of inkjet printers compared to dye sub, the varnished print will have a colour gamut far exceeding what the metal prints produce.
Is there any way to ferrotype a water-based varnish coating for an ultra-smooth surface, as you could do with a gelatin coating?