I had some of those square buttons replaced on E3630A supplies that were within the serial number range specified on the service notes. It took a lot of effort to get them, initially, because there wasn't a process in place to fulfill the service note. After a few months of back and forth with a handful of people at Keysight, I finally did get the replacements. Hopefully, it's easier to get now, at least for power supplies covered by the service note.
For the E3620A, I'm not sure if the buttons are the same. The square ones look like the same ones that are on the E3630A.
HV, I look forward to seeing your DIY buttons. So many of these supplies on the second-hand market have broken or missing buttons.