There is a "bulb" setting of sorts on the X-S1 that allows specific shutter times at 1 second intervals to be set. If 15 seconds is too fast but 30 seconds is too long, you can try, for example, 22 seconds or 18 seconds or 20 seconds or 19 seconds until you zero in on what works best. But the longest possible shutter time is 30 seconds (actual exposure time of 32 seconds, see Is there a sane reason why ¹⁄₁₂₅ is not, instead, exactly half of ¹⁄₆₀?) and that is only available at ISO 100. As the ISO gets progressively higher, the maximum shutter time available gets progressively shorter.

This is not all that uncommon in cameras from a wide variety of manufacturers that have sensors in the 2/3" size range. Packing that many pixels into an area that small is a design compromise that rears its ugly head in the form of noise. When shooting in bright conditions there is enough signal (light) to adequately overcome the noise. When shooting in low light environments that require longer shutter times, there is not enough signal to offset the amount of noise produced by the sensor.

Even if you could hack the camera in some way to allow longer shutter times, you probably wouldn't get any results you would consider usable.