I could not find any spring contacts with suitable dimensions anywhere. But I did manage to fix my dock by replacing the broken contact with a pogo pin instead. The pogo pin base was a bit too wide for the plastic housing that the springs poke through, so I had to widen the hole a bit with some emery cloth. It's not pretty but it works.
https://a.aliexpress.com/_EG8hpQS
SMD type 5mm pogo pins.
They come in blocks of two but I only needed one and didn't want the black plastic housing they come in, so I broke that off with some snips.
I used a hot air rework station to remove the old broken spring and to mount the new pogo pin in its place. Then I used my soldering iron to put some additional solder around the pin and pad to make sure it holds in place.
[image|3672079]
[image|3672080]
[image|3672078]