first issue here is the differences in terminology regarding strains, vs variants.
strains are signifigantly different from each other, variants are a nuance on the same theme.
the virus strain that infects small mammals is separate from the trans specific strain that spilled over to humans.
the virus with small changes to the spike sequence altering spike structure or function is a variant.
under emergency conditions a 3phase trial is not mandatory , and would likely be a quick deliberation under normal conditions for small adjustments to the sequence, similar to seasonal influenza vaccines.