How many LEDs in total do you have to solder? If it's only 10, surely hand soldering is faster any time. How long does it take to get other tools?
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I actually solder two pin parts with two soldering irons simultaneously. Tin both pads, place component and tack on one side, apply flux then apply heat on both sides. Part aligns perfectly automagically and no need to place components accurately which I find the most tiresome part. But this technique only seems to work properly when the board is preheated to ~100C, but that could be because I only tried it on a 6 layer board so far with two solid inner ground planes.