Given the situation described, an FX-888D should be able to handle that. So I'm thinking along the lines of tip quality, technique, and quality of supplies (wick, ...) sorts of things.
Definitely give the adding some leaded solder to the joints method a try (lowers the melting point of the lead-free stuff used to assemble the PCB).
A solder sucker can be useful as well.
Also make sure the tips fit the heating element (not sloppy); this is one of the reasons why you want genuine Hakko tips, and that you're using a quality wick (Chemtronics, Techspray, Multicore), not an eBay special made in China (genuine Goot is good stuff <from Japan>, but what's found in the US seems to be mostly counterfeit).