To get the cap off you run a coarse threaded screw through the hole and up against the stub axle end. This then strips out the hole in the cap, enlarging it.
You then get a chisel and tap at the lip of the cap where it meets the hub, seperating it with a little damage, and walk around the cap, removing it, in the conventional manner.
If you find yourself loving the idea of the screw removal method and wishing it actually worked, take a cap and braze/solder in a small nut inside that a machine screw would go through. This nut will not strip and will actually walk the cap off.
As for wheel bearing play, the oem spec is absurdly loose according to any bearing manufacturer I know of. A loose bearing beats itself silly, and it makes the vehicle unstable to drive because the wheels are flapping around. Personally, I tend to follow the recommendations of the bearing manufacturers that generically call for zero play at the loosest, to some pretty significant drag. With a Spitfire, I go for zero play. It makes an appreciable difference in the handling and ride of the vehicle.