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No, because you can’t have something have that precisely defined of a position.

you can - you merely need enough energy to precisely define it (as according to the heisenberg uncertainty principle)!

Unless...such an energy exceeds the Schwarzschild radius...

So you can’t.

You can't halve a Planck length so you're limited to ~1.6×10^−35.

I think current theories break down at less than a Planck length, but they are not constrained to integer multiples of it.

Relativistic speeds can contract the length of any object as measured from an outside observer. If an object the size of 1 Planck length travels fast enough: you won't be able to measure it, as from your position it would be smaller than the Planck length as it passes by.

It's not impossible (afaik) for things to be smaller than the Planck length. We just don't have the ability (maybe ever) to measure something smaller than this limit.

Now, good luck finding something the size of 1 Planck length, and also to accelerate it to relativistic speeds.

By definition you can if you accept it's continuous.

No, because space might be continuous, but that doesn’t mean the uncertainty principle and the Planck limit disappear..

The Compton wavelength will probably cause trouble for the storage scheme long before gravity becomes a problem.

Those are only relevant for decoding it.

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