All the strings on any short scale are floppier than on a 34" bass. That's just physics and part of the short scale experience. String-through is irrelevant. String choice can mitigate this, but if you absolutely need a stiffer feel, don't buy a short scale bass.
I know this has been said to death, but string tension is different from string-stiffness. Hex-core strings are a lot less flexible/stiffer than round-core at the same tension. With the right strings, I don't experience any floppiness on my short-scales, but with Thomastik Ti flats, I experience extreme floppiness on my 34" scale bass. You are right though, that given the same strings, a short-scale is going to be lower tension than a long-scale, but that doesn't necessarily mean all short-scales will be floppy. Chromes are one string that I find stiff on both long and short-scale. Dr Low Riders also felt pretty stiff to me on my short-scale.

