I started from one corner of each IC with a little bit of solder on one of the pads. As soon as that corner was secure I jumped to the corner opposite of he previously soldered pin. Solder that pin. This method allows you to tack down the IC for hands free soldering. Once the IC is tacked down, the rest of the pins are easy enough. Keep a solder sucker handy just in case you bridge any pins. Move fast and keep any heating of the chip as minimal as possible.
Here is the PCB with all required jumpers installed. The jumpers are made from salvaged leads left over after soldering components.