Hello - I have a kind of workaround that I found. I basically create a gallery but that's the only thing in the section, I then save the section. You can then just add the section on the page you want the gallery on. Once you bring in the saved section with the gallery on your new page just copy and paste the gallery onto whichever section you'd like. After pasting the gallery where you want it on your page, delete the saved section (or leave it if you want a big gallery on the page). This way you can just add a saved section, copy the elements you need for your page, then delete the section. Bada bing bada boom!
It's really not ideal but it's a quick way to do it without having to dig into code. Saved sections has really made my entire workflow efficient with 7.1. Any type of element I know I will need to reuse elsewhere I always create it on a blank page, save that section and then use on other pages on my site. I actually have a disabled, unlinked page on all my 7.1 sites, and I will create sections with media or written elements I know will need to be used or repurposed elsewhere on the site.
All this being said - if anyone who can do anything about it sees this - please add a "use existing galleries" feature to 7.1!