I totally agree with Rob. JPEG file size limiters should not be used unless you absolutely don't care about image quality degradation. I can't imagine what application where that would be acceptable.
JPEG compression efficiency at any given Quality setting varies typically in the range of 5:1. Using a file size limit means the images with the least detail will be saved at very high quality setting (i.e. 90-100), and images with the most detail will be saved at much lower Quality settings (0-50). This is the exact opposite of what you want to do!
Unless you use a large file size limit some of the exported JPEG images will probably have visible JPEG artifacting. You are better off determining your threshold of acceptability for JPEG artifacting (i.e. Quality 50-70?) Then use that Quality setting for your exports without restricting files size. The resulting "average file size" will be less than using a larger file size limit.
Tips for further reducing files size of Exported JPEG images:
1) Use conservative sharpening settings in the Develop and Export modules (i.e. don't over-sharpen)
2) Use sufficient Color and Luminance Noise Reduction settings to reduce visible noise in the image.
3) Make sure "Remove Chromatic Aberration' is checked in the Lens Corrections Color panel.
Following the above suggestions can reduce exported JPEG file size by 50% or more, especially for high ISO raw image files.