Here's a paper that looks at 15 lensed quasars' time delays and comes up with a value for H of 70 +/- 3. This value is independent of the WMAP data, or similar measurements.

The paper discusses the outlook for studying many other lensed quasars to confirm that the value of H is the same in all directions, and to refine the value arrived at here.

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It is interesting how the spread in values for the hubble parameter has been shrinking over the years. Few groups are still getting results of Ho in the 50s, but many more groups are getting results in the 70s. Even Sandage et al, a proponent of a lower value for Ho, recently published a paper which put Ho at 62. So I think, unless some unlikely trick of nature or coincidence is at work, that the Hubble constant is almost surely between 60 and 80-- and probably right around 70.

If the cosmological expansion accelerated 5 billion years ago, shouldn't there be different values for the coefficient of expansion before and after the beginning of the recent acceleration?

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For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?

Yes. I'm not sure what the values are, but the older values of H would be smaller than the newer values by a few percent.

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Are our instruments good enough to detect other variations of the coefficient of expansion that may have ocurred prior to 5 billion years ago?

__________________
For those inclined to oppose human meddling with the structure of the universe or the composition and configuration of objects and groups of objects within the universe, consider:
Whether there is a limit to the magnitude of a modulation of chaos below which order remains invariant? Or, is order but a fiction invented by perspectives applied over finite, however large, time intervals?