Hi,
Thank you for offering a good solution.
I admit, I am intimidated by command line but this may be a good opportunity to learn more about Imagemagick.
I went ahead and finished this project using "Save for Web" on each image individually and working with the "Optimize for File Size". I sped up the load time in the Image Ready interface by using a batch command to resize all the .tifs to the final pixel dimensions in a temp folder.
I found that that each time I saved the JPEGs an additional 3kB+/- was added to the predicted file size, so I used a "Optimize for File Size" target of 120kB to make sure the file sizes remained below 125kB.
Regarding JPEG compression; as has been suggested above, a wide range of "Quality" settings were used to conform all the images to the 125kB target. For example; some images, such as interior scenes with smooth surfaces, were compressed at a quality setting of "50" while exterior scenes with lots of leafy texture, would not reduce below 125kB value at the "0" quality setting.
When confronted with the impossibility of shrinking the file size below 125kB at the lowest "0" quality setting, I used Topaz Detail with varying negative values for the "Small Details" parameter, and occasionally used a slight reduction in the "Medium Details" parameter, to allow the "Save to Web" function to reduce the file size below the 125kB threshold.
Thank you.