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I'm disappointed a gas giant planet wouldn't really float in a big enough ocean. But an icy planet might, or a small rocky planet with enough caverns in it. But how big could they be?
The deepest ocean would be a globe of pure water; we have one of those in the scenario. Tangaroa is a ball of pure water, about the biggest you can get without having high-pressure ice at the centre.

You could, I suppose, float a ball of low-pressure ice in such an ocean, but the mere presence of so much ice in that sphere of water would change the characteristics of the world - the low pressure ice would float on the surface of the water, and the increased mass would cause high-pressure ice to form at the core- so you'd end up with a triple-layer world; an icy outer layer, a water ocean and ice again at the core.
A possibility that may result from the destruction of the stellar primaries is that any planets formed pre-supernova might have been blasted into bits by the cataclysm(s), and then recycled into new worlds afterwards. A rocky planet with a radius 1.6x Earth or smaller can avoid collecting a hydrogen-helium atmosphere, while maintaining a "reasonably" Earth-like surface gravity.

Radtech497
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