Just for an update now that I've landed in the USA: One week after entering on my CR1, I went down to my nearest SSA office and update my status, pre-filling my data online. I also had to update my name as the Bern Embassy used the German spelling of my surname. I took my passport with the I555 stamp, birth certificate and my old social security card. I had to wait about 90 minutes (expected wait time was 160 minutes, but I got through faster) and the guy at the counter was super helpful. All in all, a very pain free process!