Icing for Coconut Lemon Gateau?

[Dishwater.Hands]

I have this beautiful cake done but I can't seem to get the icing down right. My second batch is still very granulated.

The recipe:
2c granulated sugar
4tbsp water
pinch of cream of tartar
1 egg white, whisked stiffly.

Heat the sugar, water and cream of tartar until dissolved stirring. Boil to reach 120c/250f on a sugar thermometer. Remove from the heat and when the bubbles subside, whisk in the egg white until thick.

Now, I did this two ways and neither way has worked. I followed the recipe exactly. The first way I did it was stirring the sugar occasionally until it dissolved, on a mid heat setting and I'm sure the cream of tartar caused it to bubble and it didn't carmalize like it would if I hadn't used cream of tartar. I let it settle and then put in the egg white after it was whisked stiffly and whisked until the icing was nice and thick and blended smoothly. It looked lovely-- glossy and light. I tasted it and it had the consistency of wet cement. The other way I did it was not stirring it as much, maybe once before it hit 250f and I had it on a much lower heat. The less stirring and lower heat was the difference the second time and while it didn't turn out as gritty- it's still not the consistency I figured it should be.

Can you think of anything I can do to make this a bit better? It's sorta gross. Or perhaps, I should use a different icing? I was thinking of a light custard sandwiched between the cake.

 

[Selkie]

Try using super fine sugar, otherwise known as castor's sugar or Baking Sugar. Mine comes in a carton like a half gallon of milk. It's still granulated but less than half the size granules as regular table sugar.

 

[Dawgluver]

I couldn't find super fine sugar for a cordial recipe, so I ran regular sugar through the blender.

 

[Dishwater.Hands]

See, I was gonna try caster sugar but I wanted to follow the recipe. But after trying a bizarre recipe that called for shortening and caster sugar, I ran out. I ended up taking a recipe that called for whisking egg whites, 1/2 a cup of cornstarch, 3/4 cup of sugar, pinch of salt and 1/3 cup of water in a heat proof bowl over simmering water until it dissolved and then blending on medium until glossy peaks, adding 1/4 tsp of vanilla while blending on low. It came out lovely.

Thanks for the tips, though!

(PS Dawgluver-- caster sugar is hard to find where I'm from, but I found it at the bulk barn for a relatively decent price.)