If you dropped something it would simply stay right next to you, even if you were accelerating - both of you are accelerating at exactly the same rate.
If you want a useful thought experiment about physics then you need to give reasonable physics tools. Otherwise you get something like "Pretend you are an inanimate green blob. You can't climb a hill, can you? Therefore climbing a hill is an illusion."
The only type of acceleration that is undetectable is gravity - and gravity will effect the dropped object exactly as much as you.
Dropping something was only one idea, but feeling pressure is much simpler.
And as shardling said, a reference frame isn't a physical thing that is created and destroyed - it's simply the zero point for your system of measurement - but the measurement would work just fine if you started with any number, zero is just convenient.
I may have missed the point of dropping an object, though. I thought the idea was to create a physical point we could anchor the coordinate system to, and in that way be able to measure acceleration.
If the force is external and doesn't apply pressure then you have to drop an object.
If the force affects the entire universe the same way then that's aether and can't be measured / doesn't exist. But that was not the kind of force I was using to disprove "you can't move".
What kind of force is external and doesn't apply pressure, and also doesn't affect the dropped object? There is no such force, and therefor no such test.
You can't. There is absolutely no test that can tell you this.
You can't "drop" anything - whatever force is accelerating you also accelerates the object, so letting go of it tells you nothing.