You are correct that carbon dosing without a skimmer won’t work well, the bacteria stimulated to take up the nutrients would just break down into nutrients back into the tank rather than being exported as skimmate.
Without a skimmer you will have lots more nutrients to deal with since food/poop won’t be removed before it breaks down into nutrients. You also will lose the gas exchange advantages of a skimmer, which are huge in my opinion.
DSB or large MP block can keep nitrate levels in check, but since it doesn’t remove biomass, it won’t do anything for phosphates or other nutrients that build up. So now you have to set up a phosphate reactor. And a carbon reactor if you weren’t already planning it, since you’ll have more additional organics building up. You could just do more water changes to keep all of this in check, but then why bother with the DSB?
Another problem with a DSB is that you have no real control over what it is doing or how much it is doing it, sort of setup-and-pray rather than titration to measured nutrient levels like other approaches.