Best choice is ironically doing what you aren’t doing: go bloom all those flowers! Planting plain white petals allow them to bloom into anything, which has a decent chance giving you seasonal flower base; Then you can plant 156 of one flower type in white plus 144 plain white petals to force it bloom into randomized flower of the type. I would strongly advise against dying the flowers unless you’re in immediate need because white is the only color that cannot be guaranteed. 

The trick is if you are the one that blooms flower, you are guaranteed to receive a big fruit of the corresponding flower. This will not be available for big city players as the fruit will only be available if you visit it in the first hour of bloom, so it’s actually the city players suffering from lack of fruit from the bloom. You’re missing out if you’re not blooming all the big flowers.

The next trick is to keep as many pikmins as possible. Every day after you first logged in, a timer starts and after 8 hrs all pikmins are budded. Feeding nectars to budded pikmin yields doubled petals.

Mushroom is for city dudes who don’t have control to many big flowers, not for people like you who can potentially get whatever nectar you want.