The sequencer is now fully assembled apart from the MCU and SPI EEPROM not being mounted, according to the instructions. Video and photos in the post!
The buttons were easier to fit than I thought they would be; Just push them all in and keep pressing the button tight to the board and solder just one leg, verify the button is flush against the PCB and then do the rest of the legs.
It is probably also a good idea to solder the button LEDs last after you’ve verified that the buttons are mounted OK. I also noticed that the LEDs can move vertically within the button so just go over all the buttons and push the LEDs down so they sit at the same hight. Does not matter functionality wise but it looks neater.