I think that our estimates are too dependent upon assumptions that go into the FWR equations (and the FWR model itself) in ways that are insufficiently confirmed by experiment to definitely put a value on the cc that will stand the test of time.
Issues such as: Could an extra-horizon mass distribution have an impact, are imhomogenities sufficiently great to make an impact, and are all of the multiple different methods of estimating the Hubble constant mutually consistent within their error bars, leave me agnostic on the issue.
In my mind a pheneomena that would appear to be a varying cc is wrong as a matter of definition. Either you have a cc which is constant, or you have some other phenomena which varies, or you have both. Constants don't vary. If cc is part of the GR equations then is must be a constant and not a function, because it arises as an integration constant. But, if it varies, it is a function.
Could there be dark energy distributed in such a way that it mimics one cc at this time period and another when the universe was 1% of its current age? Probably. But, in my mind, that wouldn't be a cc.