I'm trying to make a DIY instrument roughly based off a pedal clavichord. I'm trying to figure out what strings to use for the lowest notes, the lowest of which will be C1. I don't want these low notes to sound as 'bassy' as a bass, but brighter, like a piano or a guitar. I imagine guitar strings are brighter because they're thinner and shorter, but this won't work for low notes. I imagine piano strings are brighter because... Well, I don't know. They're longer and thicker, both of which you would expect to give a bassier sound, so it must have to do with their incredibly high tension. I am limited by length because the longest commercially available electric guitar or electric bass strings are 40" usable length (which is the low end of the spectrum of piano bass strings). I don't want extremely high tension because I'm just using wood, not a cast iron frame. I can experiment with gauge, though.
My current plan is to get a set of DR LMR5-130's and see what they sound like strung up on some zither pins 40" apart in a fence post, with a single coil guitar bridge pickup underneath, run into a guitar amp, I guess, cause I don't have a bass amp. Though I do have an acoustic guitar amp...
So yeah, I was trying to find out if upright strings would get me closer to what I'm going for than electric strings. But of course, the problem is that they're way too expensive for this phase of the project in which I'm just testing things out.
Ah, now we can give you more useful answers.
The short answer to whether upright or electric strings will get you closer is that this is probably the wrong phase of the project to find out. A longer answer is, well, a bit longer
Regarding the problem of how to get the specific timbre you're after, you're trying to build on speculation: you're starting with the assumption that the difference is entirely in the string design, without having verified it. The best advice I can give you there is to back up a little, and frame the problem differently.
The question "what factors make the bass notes in a piano sound brighter than those of an upright bass?" will take you down fewer blind alleys, especially if you factor in the difference between the way notes are sounded on a bass, a piano and a clavichord. And that's before we get to the part where you're designing an electric instrument, but using the sound of acoustic instruments as your reference point, or the bit where neither piano strings nor (most) double-bass strings are designed for use with electromagnetic pickups. Even that question is a matter of optimisation, though, which leads to the next bit...
The best advice I can offer is to forget about string-types for now, start* with the simplest proof-of-concept prototype, learn what does and doesn't work (both in the design and in how you went about building it), then make another one that builds on what you learnt. Rinse and repeat until you're close enough for all practical purposes. At
that point, compare the timbre you're getting with the timbre you want, and seek out ways to close the gap. And then you start testing alternative solutions, comparing their results, and iterating on
those results. This is the point at which the differences between a piano and an acoustic guitar will come into play
if they're relevant to solving the problem that you have at this point.
One way of closing that gap might be to borrow from the piano and the 12-string guitar, and put higher-tuned strings beside each of the bass strings, to add brightness synthetically. A family of other ways live in the electrical and electronic side of things, starting with the pickups, and including the part where you don't accidentally remove the brightness without realising it. And then we have the perennial tonewood debate

The speakers or headphones you listen through will also be a factor - you'll get different results just from using a bass amp, a guitar amp, or reference monitors.
*
After learning as much as you can about how similar instruments are constructed. As satisfying as it can be to find all the pitfalls and climb back out of them yourself, you reach your goal much faster if you can learn from the mistakes that other people have already made.