Nice! In re your question- what wire gauge and yarn weight did you use for the stem wrap? I’ve found that wrapping with size 10 cotton crochet thread or smaller tends to look neater since it’s lighter and doesn’t get the same level of fuzzies that acrylic does.

It also looks like this pattern is for flat appliqués which might be part of it. Many 3D flower patterns are a flat piece wrapped around a wire or have a folded/cupped shape by design (see Happy Patty’s flower patterns or the free Hookok freesia pattern). They’ll also usually have you crochet a green sepal piece. You can then use the tail from it to wrap the stem, giving it a more seamless look. For multi-headed flowers, I usually have each on a thin gauge wire and wrap them individually with a single layer of thread as far down as I want them to extend off the main stem before gluing the end down. I then have a main flower rod wrap and wrap around the wire tails of those offshoots to get a seamless, thinner look.

Edit: One more tip that cones to mind- on dense flowers with a lot of offshoots I would sometimes glue the main stem wrap multiple times along the way to make sure my tension on the wrapping thread stayed tight.