I have the earlier version of that iron (without the digital display).
I was using the 1/32 or 1/64 round point tips in it for very fine work like that, and while they work, I too found that a pointy tip doesn't tin and hold solder as well as a REALLY SMALL flattened chisel tip.
Look for the ETJ (0.79 mm screwdriver tip), ETU (0.38mm flat tip), or ETV, another very small, fine tip. Newark Electronics sells the completely line if you can't find them elsewhere.
Also, since I have that electroplating kit from Caswell and plenty of nickel plating solution left over from my brass engine building days, I have taken to filing my own tip shapes and then nickel plating them so they will hold up to soldering and tin nicely. The tip I'm using right now is a pointy "conical" tip where I filed the point to a little flat and then plated it. If you're not into plating DO NOT JUST FILE THE TIPS!! They are iron clad or nickel plated and if you file the plating off and don't replace it, they will oxidize, corrode, and in general be a bear to tin or use after that.