@lupyuen this is what I was going to suggest, but the putty farther down. In fact. if you put it so far down only a mm or so of the wire leads produce from the bottom it should be able to rest on top comfortably. A low center of gravity plus less wire length so less bending I think should do the trick.
Honestly I'm surprised you dont just have a 2x row header you could use instead.
@lupyuen the key will getting them spaced just right in the clay I think.. but if you do without much showing I think it might work nicely. Good luck.