I initially moved my Sim into Bargain Bend, then used the phone to move to/bulldoze Oakenstead. I chose that lot because both the lily and snapdragon plants are available there and angelfish can be caught on the beach across the street. The key was to avoid leaving the lot at all so that plant growth times were not interrupted. I chose the Homey and Great Soil lot traits. Great Soil increases the speed at which plants grow. I'm not sure of the exact percentage, but it's significant.
After moving in, my Sim immediately went to San Myshuno and bought a pomegranate from the fruit vendor. This was the only time he left the lot. He got home, planted the pomegranate, took a citrus soak bath with incense burning (12 hr focused moodlet) and then joined the Garden Gnomes. He started a club gathering and chose the "fish together" option on one of the fishing signs near the lot. Once the club started heading over to fish, I cancelled the action on my Sim and had him read gardening books until he got to Level 5. He did stop reading briefly when the snapdragon sprouted a flower, harvested and planted that. He then joined the group fishing. At some point while fishing, the club had enough points for Rally the Troops, which enabled them to continue fishing until my Sim caught an angelfish. By the end of the first day, my Sim had gotten gardening to Level 5, had caught an angelfish, and had spliced the lily/snapdragon.
I spent a lot of time watching plants with the camera zoomed in on them so I could complete actions as soon as they were available. As soon as the lily and snapdragon were ready, I took a cutting from the lily and spliced it to the snapdragon on my lot. As soon as the grafted plant sprouted an orchid, I had my Sim plant it, grafted pomegranate to orchid, etc. I seldom ran my game on fast speed because I didn't want any time to pass between when an action was available and when my Sim could do it.
I next joined the Upper Crusts for the cooking and gourmet cooking boosts, although this probably wasn't necessary since those skills build so quickly anyway. While in a club gathering, my Sim cooked and I used Nutella's trick of mining cooking for satisfaction points, plus completing Master Chef milestones, so I could purchase the Green Thumb reward. Great Soil + Green Thumb makes plants grow really fast. I wasn't worried about spending the points for Green Thumb because I knew I had a couple of days to make up the 1500 points for the Potion of Youth and I could easily get those points by satisfying cooking whims. Once I got the points for the potion, it was just a matter of time waiting for plants to grow. I set up an easel and had my Sim paint while right next to the plants and the very moment a death flower sprouted he quickly harvested it, cooked his ambrosia, and ate it.
I should mention that as soon as I got Green Thumb, I had my Sim talk to all of his plants because the effect starts once the Sim interacts with a plant. I wasn't sure if talking would count, but nothing was ready for watering or weeding so I figured I may as well talk to them in case it did work!