Before working on the inside is there any problems with the inside of your horse? My horse' coat lost its shine and turned out he had anemic. Maybe it might be worth to get him/her checked out?
If theres nothing wrong some tricks i were told were to put some Guinness in their feed (dont think you get our Guinness over there do you?) or some eggs stirred into their feed. Or mollassed chaff
Mine live off pretty average meadow hay and a couple of scoops of bulk pellets (nothign fancy) unless they NEED different feeds and all of them have a brilliant shine on them- and no they're not rugged unless they're my comp horses or clipped.
If the horse is healthy, it will have a shine on it's coat. To enhance the shine, there are supplements you can feed them, or add oil/sunflowerseeds/flaxseed etc etc. in their feed.
Being a roan, it will make it harder to see the shine on the coat, much like greys they never look truely shiney, so just go all out with your grooming, when you wash do it either 2 days befor the show then RUGS to keep the coact flat but don't let him sweat as this will dull the coat further. The day of the show you can spray them with shine products, just don't go over board with it and avoid the saddle area or you'll end up sitting on his backside You can also wipe him down with a soft cloth, this gets rid of any surface dust and will encourage oils to come to the surface of the hair follicle.
I found this stuff at my local tack shop and it made my horses SO shiny and glossy, I couldn't believe it.
I did definitely have to be careful about the saddle area and be sure to wash it off the next day so they don't get dirty, but I had no idea they could get quite that shiny! it's silicone free and it conditions.