We see around one base pair mutation per host transmission, so that would likely already put us outside 99.9% similarity even among humans with coronavirus wouldn't it?

Rough estimate:

(29,000 base pairs, just assuming 3.5 days between generations, 395 days since first affected person (probably it was a bit more), would be 112 mutations = 99.6% similarity)

And I think we'd expect more changes to be selected for in the early period of host adaptation.