I remember Reb Dovid also said that if Reb Berke would see mehuderdike tefilin, he would right away put it on, because maybe it was more mehudar than his own tefilin that he put on that day.

Yes he told us the same. He specifically mentioned about saying Shnayim Mikra on Friday.

Another example of a Chumra was that he saw someone opening the Tefillin knot before making the Bracha (as many people do today), and he immediately began doing the same.

One example of many chumros.
He once told me, that “thinking back”, he doesn’t think Reb Berke was on the top of the wanted list – unlike they thought then.
(Didn’t understand what he meant, thinking back.. But that’s what he told me. [Interesting to note, that they did send Reb Berke later to Jail while trying to escape])

He told me once that one of the chasidim spoke to Reb Berkeh about doing shnayim mikra in one shot, and he immediately took that upon himself