Can juicebox be adapted to tell the browser to load the images sequentially (by name)?
No, unfortunately not. The only control you have over the preloading of images is the imagePreloading configuration option (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section).
I think your issue is a direct consequence of setting enableLooping="TRUE".
Normally, Juicebox-Pro will preload both the previous and next images in the gallery (both images adjacent to the current image) so that they are ready to be displayed should the user click the 'previous' or 'next' navigation button.
If enableLooping="TRUE", then the previous image will be the last image in the gallery (in your case No. 9) and Juicebox just seems to preload this before No. 2, No. 3, etc.
As you are aware, large file sizes and a slow connection are also contributing factors.
As an example, if you were to create a gallery using JuiceboxBuilder-Pro with all default values, then the resulting image sizes would be around 120KB. With even just an 'average' connection speed, this would probably not be an issue.
However, real-life constraints (such as a slow connection speed) will certainly make a difference and you might need to counteract such factors by doing thing like reducing your image sizes (especially if you know that your gallery's target audience is likely to have a slow connection).
The other option would be to set enableLooping="FALSE". Perhaps not something you'd like to do in an ideal scenario but a compromise that would help to resolve your problem.
Please also see my notes regarding Muti-Size Image galleries in your other thread. They might be of interest to you.
If you'd like to suggest an idea for a future version, please feel free to post in the Feature Requests forum thread.
This keeps all the ideas together and ensures that they are not overlooked by the developers.
I do not know the likelihood of any suggestions being implemented but this is certainly the best place for all ideas.
Thank you.