Rather than water is there any solvent that can better dissolve or disperse GaN?
Gallium nitride density (6.15 g/cc) is higher than any solvent or even than any known salt solution. Clerici solution (a saturated solution of thallium formate and thallium malonate) has a density of 4.25 g/cc at room temperature and ~5 g/cc at 90 degC and as far as I know has the highest density among known aqueous solutions.
As for solutions: Any liquid that dissolves GaN does it, as far as I know, by decomposing it (to a Ga(3+) salt and ammonia or an ammonium salt). Essentially it would be a solvolysis reaction, driven by the extreme basicity of the nitride ion.
Amending my previous answer: You may be able to disperse GaN in liquid gallium (6.1 g/cc), or if you want it to float on top (also not to worry about the liquid freezing overnight), in galinstan (6.4 g/cc). Galinstan is a Ga-In-Sn eutectic that is used, among other uses, to replace mercury in medical thermometers. There are also a variety of heavier liquid alloys based on heavy metals such as Bi, In, Sn, and if toxicity is not a consideration, Pb, Cd and Tl. All those however melt considerably above room temperature and are likely to be inferior to Ga and galinstan with respect to wetting GaN.
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