If you have a Viscount seat it is probably over 25 years old. It may have broken down padding and be 'sway back' like and old horse.
It's not so much the width or narrowness of the saddle that makes it uncomfortable, but the match of that dimension to the width of your rear and where on your ass and saddle you like to position yourself. Also, the shape of the saddle and amount and type of padding affects comfort.
Some saddles are flat, some are curved and roll off at the sides. Some taper to the nose faster than others. Some have channels or cut-outs to relieve pressure. Some are well padded and some have very little padding. Some have a radical nose drop.
The truth of the matter is that many riders will find the narrow, hard saddle more comfortable than the softer, wider design.
This is an area in which only you can make the correct call. There is not much valid advice can be given over the internet when it comes to saddles. Your best bet is to go to a bike shop and sit on a few types. Perhaps you can ask to take a short test ride or two on a couple of their demo bikes.
Some shops offer a low cost (or free if you purchase a saddle) fitting system of some sort. I'm skeptical of them, but they may get you a 'start' to finding something more comfortable than your old Viscount saddle. Both Terry and Adamo manufacture good 'comfort' saddles, but you may not require anything in the 'comfort' line. You may only need a better fit, more or less padding or a slightly different shape. There's a few variable here, so don't be afraid to swap onto a few different models.
As you suggested, varying your position on the bike helps, although I think we both suspect your seat is still not a match to your body. Racers and tourists that spend many hours in the saddle are fitted on their bikes to carry more of the body weight on the hands/handlebars and shift their weight to the pedals, hands and saddle often and automatically.