installing vaporstat - which one to use

We agree on the 16 oz vaporstat, and we also agree on the method you described with a low pressure switch with a timer to extend the off time once the low pressure switch opens.

I added the dysfunctional-ness of the Pressuretrols and Vaporstats, enough complaints on here over the years. and the Mercury version worked better.

I also added a duty cycle / frequency based timer method that does not require any additional pressure switching device as an option.

And to independently verify the equipment he already has.

First off here, there are actually two differences between vapourstats and pressuretrols. Well, three. The first is obvious — the vapoustat (either model) can be set to a lower pressure, and is more flexible as to setting the desired differential. The second is by no means obvious: because of the way the vapourstat is made, it is considerably more precise. This is does not necessarily mean more accurate! What it does mean is that the variation between the pressure at which the vapourstat will operate, either cutin or cutout, varies very little from cycle to cycle, while a pressurestrol varies much more widely. Either one can be calibrated, if desired, to the same accuracy within their respective pressure ranges. The third distinction is also obvious: the vapourstat is more expensive.

As you have doubtless figured out by now, there is considerable diversity of opinion, both within the trade and from knowledgeable hobbyists, as to the best way to operate a steam system, particularly one with an oversized boiler. I have rather definite opinions, but they are mine and not necessarily any "better" than some of the others you can read above.

You would want to do that

The steam pushes against the water which then moves and pushes against the air between it self and the diaphragm in the control.

The water acts as a piston.