I don't see much, if any, advantage to using the alternate methods you mention to avoid using wood ties. I would use the conventional wood ties. They would be authentic, and mine tram tracks often get by with fewer, more widely spaced ties than more conventional tracks. So the widely spaced wooden ties on a mine tram would be authentic in appearance and function, plus it would limit the number of ties needed. Plastic ties would not look authentic, and would probably cost much more than wood ties. In either case, with ties used in a display track, longevity will not be an issue. Mine tram ties often are relatively primitive in their cutting and shaping. They are also often relatively large in cross section compared to rail size. Maybe used standard gage ties cut down in length could be used. Just lay them on some crushed rock or gravel acting as bedding and ballast, and use soil stabilization fabric or similar under the rock to keep weeds from growing.