I just use an ordinary iron with 1mm tip and leaded solder (I know...) I use a flux pen too.
I can usually get about 90% of the pins done without any bridges, and then just use an ordinary solder pump to remove them. Works well with AVRs, some other ICs may be a bit more heat sensitive. I think you really need leaded solder too as the melting point for lead-free is too high.
My fingers are stiff with banned but somehow I still manage to solder these fairly small pins so it can't be that hard
I have done about 40 Retro Adapter boards this way and maybe 20 other ICs for prototypes over the years. In the future I am thinking about asking SeeedStudio (who do all the PCBs) about buying stencils as those are what they use when assembling the same Retro Adapter boards.