Yes it is a lot of waiting. You can at most craft 1 Ivy pic a day with 2 Ivy hut visit (unless you gem) but even if you do, there's watchtowers, chickens and skunks, all not guarantee drops either
I'm on goal 10, with 0 Ivy's drawing, 2 Thomas, 1 Thurston
And I see goal 12 needing so many, 4 each! isn't that 4 days of waiting just for Ivy Hut.