I have viewed your web page in several browsers (IE10, Firefox 20.0, Chrome 26 and Safari 5.1.7) on my PC and do not see any galleries at all (due to your modification of the 'juicebox.js' file).
There is no reason why you should not be able to display 4 Juicebox galleries on the same page.
I regularly use jAlbum and the Juicebox Skin to create multiple-gallery albums (with a JavaScript tree menu which switches out many more than 4 galleries on the same page).
I have tried using the JavaScript you posted with 4 of my own test galleries and all worked fine. I can continually switch between all 4 galleries and have not yet been able to replicate the problem you describe. The only problem I encountered was when resizing the browser window and not refreshing the page (where the layout is incorrect) but this can be solved by setting the dimensions of your 'juicebox-content' divs using inline CSS (as documented in the 'Using Percentage Heights' section here).
Although my testing shows that your code seems to work OK, you might like to try using the Juicebox-Pro API's showGallery() method to show/hide your galleries.
Alternatively, you might like to try loading each gallery as it is selected (as the Juicebox Skin for jAlbum does) rather than load all your galleries at once and then hide/show them selectively.
Once you get your web page back up and running (by reinstating the 'juicebox.js' file to the stock version from Juicebox-Pro v1.2.0), please post back so that I can take a look at your web page for myself and please let me know what browser(s) you see this problem in.