I'm also in the shelving started games dilemma. ( ´◡‿ゝ◡`)
If it's a game with a really engaging common route, I can usually remember 70% of the details, so it depends on the game.
But! If it was a really winded, drawn out beginning that maybe wasn't so enrapturing, I might replay it...but..love interests routes do an okay job at re-summarizing the prologue so I don't feel I've lost much if I choose not to replay.
I will say if I completed a route, unless I LOVED it, I'll probably never replay before I slough through the rest of the routes or shelve it once more.
So I'm kinda in the start over if you want or just jump into your love interest route, the details aren't going to make or break you loving your route as they'd probably go over it once or twice...or over and over again....ᕦ(ò_óˇ)ᕤ