Hello Curtisa,
Thanks for your very detailed answer and the Wikipedia link. Yes, my first thought was to use flatwound strings, however, they are very hard to come by here in Europe and also very expensive. I could cannibalize existing string sets with flatwounds, but it would simply become too expensive in the end.
There are no strings sets for electric uke available on the market, at least I've never seen one. Probably because it's still such a rare instrument, most uke players prefer nylon strings. Another issue is that there is no standard tuning for ukes larger than concert and soprano. Some tune GCEA, some tune DGBE, some tune in between. The reason my choice of strings seems to give a non-consistent tension is because I sometimes tune differently: CGCE for slide, DGCF for jazz & bossa, CGCG and CFCF also good for slide, CGCF for oriental music etc. So the string gauges I chose are all in the neighbourhood of 15 lb, plus minus depending on the current tuning. I always refer to my tuning as Chicago (DGBE) as a point of reference that is easy to relate to for other uke players as well as guitarist, but I actually play some of the other tunings more often.
Most electric uke players will simply cannibalize an electric guitar string set, which is what I did before. However, I did not get the exact gauges that I wanted and also the overall tension was too high for my taste (20 lb, similar to an electric guitar with 011's). So I wanted to put together a custom set with the D'Addario singles to get a more equalized tension across the strings, as well as more bendability and less calluses. I went for 15 lb, which I would consider "the middle road", since it's right between the tension of a set of 009's and a set of 010's on a standard size electric guitar. You compare with a set of 013's, but I've never seen such a set for electric guitar, sounds more like in the territory of acoustic guitars. It would be very hard to pitch bend indeed, and I don't think the neck of my uke would hold up (already 20 lb was quite a strain).
Anyway, the strings I put on do not feel wobbly at all, no intonation problems or anything. In fact, they sound a lot better that the 20 lb set I was using before, and are a lot easier to play. Only the 026 presents the above problems. The string actually feels like it has a higher tension than the 032w I was using before, although this is obviously not the case. However, this feeling of tension in the string might actually be stiffness, as indicated in the Wikipedia article! When looking more closely on the string, I can see that it kind of arches slightly over the nut as well as the saddle, where the other strings are kind of "breaking" at an angle. This could mean, that the string is not swinging freely, but is being restricted by a spring-like tension at both ends. Hence the chaotic bell-like overtones, or "inharmonicity", as the term is in Wikipedia.
After reading the Wikipedia article, I am convinced that the problem is simply the thickness and stiffness of the string. Here is one quote from the article: "For instance, a very thick string behaves less as an ideal string and more like a cylinder (a tube of mass), which has natural resonances that are not whole number multiples of the fundamental frequency."
The PL026 would probably work a lot better on a standard size guitar or on my tenor guitar at the same tension (15 lb), since scale length is also a factor in producing inharmonicity. So while I have not solved my problem yet, at least now I know why that particular string does not work on my uke. Thanks! :-D
Maybe I'll try reducing the tension even more, a PL024 or PL022 might do the job. I'll keep looking for the flatwounds (CG) also, but so far I have found them only at exhorbitant prices: 5-8€ per string + 20€ shipping (plus they don't even have all the gauges available)! What to do... :-/