You will be thrilled to know you are wrong then.
On the tip board you just have to change park to the one you are looking for and then select the
lightning lane you want. It won't actually give you one before 2 p.m. for a park you are hopping to.
I did exactly what the original poster is suggesting, starting at Epcot and only booking lightning lanes for Hollywood Studios. It worked great. One thing to keep in mind is you can book your second lightning lane two hours after Hollywood Studios opens.