Placing the code from the FAQ at the end of your .htaccess file (as you have done) is fine. (Anywhere outside the existing <IfModule mod_rewrite.c> ... </IfModule> section is fine.)
The layout of your web page is controlled via CSS and I expect there are likely going to be media queries and screen width breakpoints (and perhaps even some JavaScript code to determine whether or not the mobile layout will be used). Being that I am not familiar with the code or internal workings of your current theme, troubleshooting is quite difficult.
If it were my own site, I'd probably try using a different theme (at least for testing purposes) to see how things look on mobile versus desktop. Maybe try one of the default themes (such as Twenty Sixteen or Twenty Seventeen) to see how you get on.
I'm pretty sure that the answer lies somewhere within your current theme's code but without knowledge of exactly how your theme works (and decides to lay out your web page), I cannot answer the question of why the presence of a Juicebox gallery on your web page changes your web page's layout on mobile devices.
Knowing that CSS is probably somehow involved, you might also like to try changing your gallery's width from 100% to a fixed pixel value (such as 800px). I realise that this is not a long term solution to the problem (it'll mean that your gallery is no longer responsive in the horizontal dimension) but it might give you some insight into the nature of the problem. Giving a gallery a width of 100% means that it will fill the width of its parent container. However, its actual width (in pixels) might somehow be calculated incorrectly and seen by your theme as being large enough to warrant using the desktop layout. Using a fixed pixel value for your gallery's width might make a difference. It's a long shot but something I'd try for myself just out of curiosity. (I'm really just thinking out loud at this stage.)
Unfortunately, without knowing exactly what is causing the problem, trial and error seems to be the way forward.
I would certainly try a few different themes (to see if the answer lies somewhere within your current theme's code) and some fixed width galleries (maybe try a few different fixed widths) so see what happens.
I hope this at least points you in the right direction.
Edit:
I've just taken a look at the headers for your websites.
The 'no-transform' Cache-Control header is correctly set up and active on your http://dev.mulhollandgates.com/ website but not currently on your http://gateslosangeles.com/ website.
Also, I notice that WP-Juicebox in both of your websites still uses Juicebox-Pro v1.4.0.
I would strongly encourage you to upgrade your galleries to v1.5.0 (see details in my first post above).
I still think that this might help with your problem.