Hi Mark,
Welcome to the forum.
12 hp is 12 HP whether 1,2 or more cylinders. Power output from a given generator will be the same or thereabouts.
Single - one fuel injection event every 720 degrees of revolution.
Twin - injection intervals at 180 and 540 degrees, so obviously 2 in 720 degrees. That is with a 180 degree crank (one piston up, one down).
I would probably be preferring an IDI if considering alternative fuels at a later time. Di if staying with diesel or using natural gas in combination with diesel might be a choice but DI tends to be slighly more noisy, possibly.
I would be preferring an engine using the well tried and tested dimensions as used by Lister - spares are more available and probably consequently cheaper.
I would not want to be running at excessive revs to get the power - although that may improve the quality of the power produced (wave-form). Low speed equalled longevity when these engines were state of the art. Otherwise you might as well get a multicylinder modern unit.
I have no contact with CMD, other than comments on this forum as to some discrepancies in their 'pushy' advertising.
In fact, I am lucky in that I can source proper Listers rather than 'oids (all of which seem to have built in inherent faults and a deal of unwanted casting sand in many examples).
Going off grid is generally not a viable option cost-wise unless using the otherwise-wasted thermal energy for space or water heating, so water cooled is probably much more useful than air-cooled (aircooled are notoriusly noisy).
If other forms of energy are expected to be harvested (solar thermal, photovoltaic, wind, heat pumps etc) then the size of your prime mover may, or may not, be adequate for your needs. Depends how frugal you want to be, how much power must be available along with a multitude of other factors.
6 kW into a battery would very soon fully charge it. Running more continuously with a 6/1 might be a better alternative and purchase a larger inverter(again there are efficiency issues in charging/discharging bateries and converting from AC to DC and back to AC from you bartteries. Have you seen any off-grid set-ups? I would recommend this before embarking on your own sytem if at all possible - there are all sorts of different ways to achieve an unsatisfactory system.
There are 'power on demand' systems out there (similar to the original startomatics)
So, there is a lot to think about. Mistakes can be expensive.
I would at least pass your system ideas across the group before jumping in the deep end. There are quite a few on here with lots of experience of running off-grid.
Regards, RAB