This is common with Trangias. I used to find the same in the UK when I used them. My miniature alcohol stove does the same. I've never found a way to prevent it occurring, though it can be made easier to clean off. Like you, I've never found a dishwasher to do anything to it, though any that doesn't come off with a cloth won't come off easily. A few drops of meths on a dry cloth may help get it off, saving your washing up water.
It's sometimes said that adding a little water to the fuel helps, though I've never been convinced. The cause is likely to be the denaturing additives rather than the ethanol itself - I suspect the ketone.
We used to wipe neat washing up liquid over the base of the pan after washing up. That made the soot clean off more easily.
Using the simmer ring makes things a little worse, as the flame from the jets is cleaner - but you'll need to use the simmer ring for long cooking or it will be too fierce.