I have shot with a tube for around 4-5 years. They are meant to help with eyesight problems, which I don't have, the reason I started using one was to increase the sight radius.
In theory this should make the group smaller, thats a theory mind.
You should really move up to a 22mm foresight and be prepared to do some serious grouping tests to find your best foresight diameter.
Clean them before every shoot, if you try to clean them straight after they are a dirty pain in the arse thing to clean. Prior to a shoot the crud has dried and easier to remove. But you must clean the tube AND THE BARREL CROWN.....Everytime
Ideally you would try one out, Barry Neesom lent me one for a few weeks before I jumped in. 1813 barrels are the same diameter rifle to rifle so if you have a club member willing to dismantle everything for you to try then have a go.
If you go down the Neesom tube route I would ask to have the thing located off of the dovetail block screw, a very handy, accurate, 6mm diameter.
Give me a shout if you want a picture of what exactly I mean.
Bing!