Removing DOC will be a problem for a sun corals, you are right. Lesser problem, if you will feed by whole organisms, like mysis, pre-washed. More if feed by chopped homemade coral food, pre-washed or not
You may try to use the same what is used for a large tank in thread Biotopes/Sun, sun, sun...
HOB skimmer and larger amounts of carbon too. Bacterial-enzime supplements like Prodibio, if you up to it. Or keep it on massive water changes, if not.
If you have a large modified Aqua Clear HOB filter that doubles size of tank, it can act as a back sump: you can hang on it Rio Nano skimmer and fill it either by biomedia or LR rubble, it helps.
I had 3L (3/4g) pico with one full sized sun coral colony, it lived on 100% water changes after each feeding, using the aged live water from 6g tank next to it.


Tired after 4-5 months.
Now have nano, 2.5g (or so) tank with small frags (less food, less pollution that for large colonies) with 7g sump, filled with LR, Matrix biomedia, ceramic cylinders, with in-sump skimmer ASM Mini, micron sock (less than 50 microns), carbon. Skimmer doesn't solve problem, neither does carbon, but together plus big water changes the water is more or less tolerable. Naturally, it takes place and is not a pico anymore:


HTH