well, I'm not into social media (never liked it), so I don't know what to recommend. But it sounds like you've found a golden nugget of a keyword, so it's worth trying to rank it.
In theory, if all your competitor has is 3 garbage links and no likes, then - by logic - you should be able to beat it with 4 garbage links and 1 like
And I am being serious here: try to get a few links (preferably not spammy ones as we're trying to rank for longer than a few days) and some likes and shares to your (similar) FB and IG posts and if you can't beat him with these you'll know something deeper is going on (maybe he's using hidden links like it's the norm nowadays)...
Anyway, as much as I'd love to help you I genuinely can't stand social media (I think I've created a FB account around 2011 and haven't used it 3 times ever since), so I wouldn't know what to recommend, honestly!
But do what I said and see if there are improvements. I would be very curious to know