The one-sided nature of "frenemies" is actually quite common. Darcy falls for Elizabeth once he gets to know her as something more than an abstract member of a dance he was forced to attend. Most of the enemy behavior in Avatar: The Last Airbender comes from Zuko rather than Aang. Rochester in Jane Eyre acts like a frenemy because he doesn't know what else to do.
The distinction matters because frankly, I've always found it difficult to believe that strident enemies can find common ground. Truly negative behavior isn't something a lover, at least, should intelligently ignore. One doesn't walk back into a situation where one can be damaged or frightened.
Zuko can be believably folded into the group because Aang never bore him animosity, leaving openings for Zuko to actually return to his baseline personality rather than the angry guy he is trying to be.Likewise, Gilbert is enamored with Anne from the beginning. In the series, at least, he literally tries to "pull her pigtails." He is less sophisticated than Rochester but pretty much operating out of the same ballpark.
Jonathan Crombie, who sadly died in 2015, gives Gilbert a perfect combination of light teasing and romantic yearning. He always wants to be close to Anne.