After using Sunbeams as my preferred rounds for many years I just installed a set of Hi-Beams on a bass this past weekend.
I may have gone Fat-Beams as the DR sound samples do sound a little thicker which I liked, but I prefer the 40-95 set which is only available in Hi-Beams.
Like you I presume, I prefer the sound of well broken in (old) strings, long after the zing is gone. The Sunbeams were at least 3 years old. It actually took me a month to finally change them because I didn't want to mess up something I was perfectly content with!
But, I recently played a used bass with very old stainless strings at the shop. I didn't care for the bass, but I loved the strings! I actually think stainless ages even better than nickel, it takes longer to get there. They hold on to that sizzle.
Anyways, I finally made the change. Definitely do not like the sound of new stainless, too hollow and zingy. But I do like how they feel, so the waiting game begins. They are on a bass that I really like, so I am in it for the long haul. Plus more of a reason to noodle on the bass for longer than I should when I should be practicing something productive, but that is another topic.
I have another bass with 6 month old Sunbeams, and they are just getting to where I really like them. So I have something to compare the aging against. Not perfect, but it will do.
Looking forward to your updates!