I’ve been in and have seen many similar situations before. Are you seeing social media as being more important than how they see social media? I understand you may know more about it than your superiors, but proving it to them will drive you mad and land even more on your plate… or they may pass it on to an intern/new hire.
If your bosses don’t see it as a priority, you shouldn’t either… because you won’t be rewarded for that extra work.
If social media is absolutely a task they desire and expect to see from you, instead of requesting extra time, do less with it. For example, you could do 2 posts a week max. Focus social media posts on announcements and even simple holiday posts just to make your profiles remain appearing active.