Rather than focussing on how it's done (inverter drive) focus on what it does (variable speed compressor)
Essentially, the variable speed allows the compressor speed to match the cooling load, so rather than a fixed speed compressor starting, cooling, stopping, starting, cooling, stopping a variable speed model can simply adjust its speed to match the cooling load, while running continuously (until there is no cooling load, or one below the minimum speed it can run efficiently, anyway.)
That has several potential benefits - one is that starting the compressor motor takes considerably more power than running it - so many starts and stops add up - this (alone) might be what someone who says "they only save power over 8 hours or more" is speaking of. However, I think any such statement is far too general to pay much attention to, given the variations in individual units (I've been considering mini-split heat pumps, and have read a lot of data sheets - some are surprisingly different even for closely related models made by the same factory...)
Additional benefits are that rather than the system blowing air that's cold, and then stopping, it blows air that's cool, all the time. Among other things, this improves dehumidification performance and is also usually more comfortable.
You state that you use your air conditioning less than 8 hours per day - but how many days a year? It is true that if the initial cost of something you use rarely is much higher then the payback for any more efficiency (from a unit costing more) is very long (and may exceed the useful life of the product, in some cases.) However, that is not something that is amenable to analysis from afar, and will vary with the initial cost, the energy cost, the use, the climate...
If your cooling needs are limited, and the cost differential is high, just look for the best efficiency among the lower cost type units, and don't worry too much about "the future of HVAC" if having it does not make personal economic sense for you. Something better may be invented before this air conditioner wears out...
Of course, if you are buying 9 of the things, you should at least consider a central system. But that may not pay off in a reasonable time, either.
I found the solution by playing with it. On the new thermostat, remove the blue and grey wires, as they are just relays to the temperature sensor. Black goes to C, and link E and AUX. In the thermostat settings, go to option 170 and change it to option 2 for heat-pump settings. This process did the trick for me.
Best Answer
It should be possible in theory to use a generic timer switch to electrically disconnect the 'stat from the aircon during certain time periods so the 'stat cannot call for cooling. Whether it's inexpensive or easy (or attractive) depends on the details of the current installation and the style of timer switches available.
A better solution would be to replace the 'stats with a more sophisticated controller that has timer functions. This solution is unlikely to be inexpensive, but shouldn't be prohibitively expensive either. It is typically easy to do this, disconnect the old 'stat from the wiring and attach the wiring to the new 'stat. Once again, the ease depends on the details of the current installation and the replacement 'stat.