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Additional data:

Below the turbopause, at 62 miles, the different gasses of the atmosphere are well mixed by turbulence, and not stratified by density.

If we assume that the relative density of HHO and air doesn't change with pressure, then we should expect that HHO will be bouyant all the way up to the turbopause, and somewhat beyond.

So I think 62 miles represents a _lower_ limit on the maximum height of the tower. At that height we can recover 16kW from the 1l/minute of water. That's only 6% of the power used to generate the HHO so this result isn't conclusive either way.

I suppose what we really need is to find the altitude at which the density of the atmosphere is equal to that of HHO at the same pressure. That would be the upper limit on tower height. Beyond that the HHO won't be bouyant anymore.