Like you, I also had a spot marked out for the wisteria trellis. I actually got Muffy just for getting the PWP's.
It took a looooooooooooooooong time for Muffy to suggest the wisteria trellis, but she finally did!
She moved out afterwards and I regret that because I never got the picnic blanket and windmill (and I'd really like those too). I may or may not get another uchi to get the final PWP's.
From the start of playing the game to where I got it, probably like 10 months. I don't need it since I don't know what it is so special of getting the Wisteria Trellis.
I've been playing for over a year and I just got the wisteria trellis about a month ago. I don't know what the "trick" is, so no clue if I did it unknowingly or not. But yeah, for me it took 1 year.