hi,
For home made pcb's I don't know of an easier or cheaper way of connecting the tracks on either face of the pcb, other than the method you are using.
The tip I would give, if your'e not already doing it, is use say 22 or 24 swg tinned copper wire, cut it over length, say, 2cm long.
Have a small square of polystyrene on your bench, about 120mm square, poke the end of your linking wire into the poly and clip the wire to about 2cm long, repeat this, so you finish up with a 'hedgehog' of precut wire links.
Insert the link half way thru the pcb, bend the two projecting wires in opposite directions as close as possible to the pcb, to an angle of about 45 degrees. So the link stays in place, as you handle and move the pcb around.
Rest the pcb on a upturned box or plastic container, so that the pcb rests on the upturned edges of the box.
You should be able to insert and bend all the link thru wires, one at a time, into the pcb without them falling out.
Then solder all the links on one side of the pcb , turn it over and do all the others, then clip off the excess wires.
What I'm saying is, if you cant find a easier way of doing an individual link, improve the way you insert all the links.
Sorry cant help with Eagle, I dont use it.
EricG