You could make all the top-layer connections using copper wires, just bear in mind that there's around 25 ground connections on the top-layer ground plane as well. You can use a star grounding method for the ground points, which should give reasonable results (or you could actually work out another routing strategy).
For the other traces on the top-layer, you can use wire on either side of the board to make the connections. Also note that at least four of those traces on the top can be moved to the bottom-layer without issue.