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Would adaptive optics help? and/or Could the rocket carry its own propellant but get power from the beam? E.g., carry its own air.

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I don't know what you mean when you say adaptive optics sorry, but yes it could carry it's own air, I'm not sure of the practicalities but it's possible.

Also there are hard physical limits on how finely you can converge a point of light, MinimumDiameter = (2.44wavelengthfrequency)/LenseDiameter This is called the minimum spot size.

'Adaptive optics' generally means lenses and the like whose shape (and possibly other properties) varies during operation to meet current operational requirements.

Adaptive optics lets telescopes compensate for atmospheric distortions to get similar performance to telescopes in space. It's also used for lasers. I don't know how it works but it sounds like it would be applicable here.

Your minimum diameter formula doesn't sound too restrictive.

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