Thanks Steve for the link, that's very helpful.
I don't think DIYLC is up to the task either, so I've done a layout the old-fashioned way, on paper.
This drawing shows the board viewed FROM ABOVE. The copper strips are on the UNDERSIDE of the board, i.e. they're not visible. The components are mounted on the top side. The transistors are shown viewed from ABOVE, with their wire leads pointing AWAY from you.
This layout is 10 strips high (strips run horizontally from left to right) and 14 holes wide, but you should add at least 2 to each dimension for safety. You can start by cutting or snapping the board to size. I hold it over the edge of a table and press at one side until it starts to snap along the holes.
There are three track cuts, at coordinates D4, J5 and H7. Remember when you're making these cuts that the board is mirrored, because you're looking at the underside.
The component mounting should be pretty clear mostly. There's a short link wire near VR1 (you could just solder the tracks together underneath, but I'm showing a jumper for clarity). R12 mounts standing upright. Q4 has its emitter pin bent outwards a bit more than normal, so it skips a track (track B) and connects to a further track (track A). Q1 and Q2 mount with their flat sides towards the right; Q3 and Q4 are the opposite. This assumes you're using the BC5x7 parts. If you're using the 2N390x parts, reverse all the transistors (Q1,2 flats facing left and Q3,4 flats facing right).
The three connections at column 14 are wires that run to the existing PCB. Look at the circuit diagram of the PCB (at the top of my circuit diagram in my earlier post) and try to figure out where to connect these wires on that PCB.
Good luck!