you got me curious, so I popped open a 4x4 single sided pcb keypad and this is what i found.
those dog-bone shapped links can be ran down and around below and inbetween the connection pins i think.
I haven't totally worked out how, but its probably possible with your type of pushbuttons.
Although it may look like spaghetti.
And another thing,
the contacts you have made, (2 parallel lines with the line inbetween), I would change that to resemble something that looks like the contacts on the pcb in the attachment.
So that they almost inter-lock. The more area of copper spread out over the whole circle below the push button contact, the more chance of a quicker/better/even contact.