Hi there,
If you want to repot your cherry now it is the time, that is end of spring, otherwise you would have to wait up to late autumn to do so.
As for the soil, everyone seems to have different opinions regarding this issue. It is also said that each individual, given time, should be able to prepare its own mix according to the tree species, the weather, the time of the year... But, as a good approximation I think you could use a basic soil mix... 60% or 70% akadama, 30% or 20% lava rock and 10% organic material (maybe peat). This soil mix would guarantee a proper drainage, together with a good water retention capability and aeration of the roots.
P.D: It is great that your cherry has responded well to the systemic treatment.