mmm... Not sure your out of the woods here.
While you state the juice didn't get inside it must of have as the only gap for the display and the system is on the same side (hinge).
So I suspect you See the juice in the display, but some also went into the system wetting logic board.
At this point I would focus on making sure the logic board & battery are clean (as that is the heart of your system). Are you up to taking your system apart? Do you have the correct tools and ESD mat to work on it?
- If not I would try locating an authorized Apple service center Vs an Apple store as they are a little bit more forgiving on wet systems.
- In the mean time put your system in a plastic bag pulling out as much air out as possible and put your system in the refrigerator (cooled not ice cold!). This will slow down the corrosive action of the acids in the juice. If you can I would disconnect the battery as well.
OK, you have the tools then you'll need to take things apart fully. Follow this guide: MacBook Pro 15" Retina Display Mid 2012 Logic Board Replacement then using distilled water (not tap water). Wipe down the areas of the logic board that look like they got hit using cotton swabs (Q-Tips). You will likely need to go over the areas a few times to fully clean up all of the juices sugars & acids. Once you do an area go over it again this time with a high grade of Isopropyl alcohol (85% or better). Let the logic board fully dry and also check the rest of the systems internals for spillage.
As for the display you can follow this IFIXIT guide MacBook Pro Retina Display Teardown. I must warn you I've tried fixing one of these displays and I ended up getting a new lid assembly as I broke the glass. Trust me I was being very careful and still messed up! So be VERY careful! Or consider just replacing the lid assembly as it's just safer & quicker. Good Luck!