Glossy fiber-based paper will only take on the "mirror" like finish if dried on a ferrotype plate, or a heated dryer that has a ferrotype surface (mirror surface). Drum type motorized dryers were once as common as salt. They were made in all sizes, from tabletop units labeled Prinz, to floor standing units in various widths from Pako, which used both electric and/or gas as heating sources. They can product the "look" you wish from fiber glossy paper. There have also been various models of non-motorized heated glossy dryers, with either a small drum or a plate with a cloth apron to keep the print against the drying surface.
If you are using a non-motorized glossy dryer, you really have to roll the print onto the dryer surface quite hard with a brayer to ensure even gloss in drying.
In general, from my 40 years of experience in darkroom, single-weight glossy fiber paper glosses best, and the only vendor for such paper is now Slavich.