Hi Kate,
Sorry if I'm a bit late to the party. I haven't been around Basses by Leo in a while either, so I'm not sure if you got answers over there.
I have about half a dozen different bass string sets at the moment. Most of them have a very quick taper from the nominal diameter down to a thinner end to wrap around the post. It is very obvious on this set of Pyramid Gold flats:
You can see that all of the strings in the Pyramid Gold set taper at about the same place. OTOH, here are TI Jazz Flats that only have a taper on the E string:
It is possible for some string sets and basses to end up with the full diameter of the E string wrapped around the post. That can stress the string and might lead to early breakage. Here are pics of Rotosound RS77s on my Lynx and my old Fender:
Notice that the silk ends at different places relative to the post on these basses. If you look closely at the second photo, you can see how the bend radius is causing a gap between the windings. I'm sure that is a weak point, but that string has been on the bass for about 12 or 13 years now.
I have had one E string break at the post, out of about two dozen basses I've owned. That string was a nylon tape wound that was already worn out when I bought the bass used in 1999. It ended up lasting until loosened and retightened it about two years ago. I mention that just to point out that having an E string that's slightly too long doesn't necessarily mean that the lifespan will be seriously shortened.
As for the types of strings I use, that really depends on the bass and they styles of music I'm likely to use it for. I almost always go with flats these days. LaBella Deep Talkin' flats have been my default set for the past 2-3 years. I have put Pyramid Gold flats on two basses, with different results. The first one is a PRS Bass IV, which is basically PRS's take on the Fender Jazz. I didn't think the sound or feel were superior enough to justify the price difference between Pyramids and LaBellas in that case, but now I suspect it was the bass rather than the strings. I've recently put a set of Pyramids onto a fretless '89 L-2K, and have been absolutely thrilled with them. My other fretless (a Guild Pilot) has a set of TI Jazz Flats. They are excellent strings, but I think I prefer Pyramids on a fretless now. If I ever find a Leo-era SB-2, I will probably go with Jazz Flats on it.
I have started buying all of my bass strings from BassStringsOnline. Their prices are very competitive, and their customer service is incredible. They answer phone calls, and can discuss the technical merits of any string they sell.
Ken