There are three very good brands Avon, Michelin,and Pirelli. I prefer the Avon's.I would be leary of a chang sung wong to, or any Chinese tire, Try a blowout, at 60mph on the front, I've survived, but with soiled shorts.
Check out campfire talk "quick release rear wheel". I posted 1-5-08. Basically I strongly recommend the Avon Road Rider AM26. Use 90/90-19 front and 100/90-19 rear. This is a fabulous choice. In my opinion you will not find a better for the Enfield.
You should replace them NOW! Aside from any discussion of profile or tread, that cracking is a sign of rubber compound break down. The chemicals in the compound that make it soft, pliable, and sticky are volatile. They are subject to a phenomenon called out gassing. This happens from heat or age. That is why race cars change tires so often. The heat from usage boils off these chemicals. When not subject to these extremes, these chemicals still evaporate. It just takes longer. Even when the tread depth is ok, these older tires still won't grip the way afresh tire will. Often, the bargain tires people get on sale or from the internet are older tires. These may not have been stored properly. A hot warehouse will bake these chemicals out of the rubber very quickly. Your tires are talking to you. You should listen.
I have a 2005 Bullet it came with Avon's. It handles so good that I lift the footpeg on easy slow intersection turns. This bike needs ground clearance not better tires .............................But If your sidewalls are cracking please buy something!
I'm not suggesting there is anything wrong with the Avon Speedmasters from a handling perspective - I was content with them until I noticed the sidewalls cracking. It's just that the Avon Roadriders were about the same price as the old ones and they do feel noticeably better to me. Like I said, though, it's not that the stock tires seemed bad (handling wise).Eamon