How to eliminate the cold drafts coming from the air conditioning vents during winter

I would also expect the new furnance to provide better heat than the old one. First thing to to is be sure you didn't arrange anything in the room different from last year. You don't have anything blocking the air registers. Check and make sure the air filter on the furnace is not clogged. If the room has only one register leave the door open so the colder air can circulate out of the room. If nothing in the room has changed contact the installer and ask them to check for any blockages or leaks that might be preventing the heat from reaching the room. It may be a problem with the blower pushing the air to that end of the house. If you have never had it done an energy audit is always a good idea. Most utilities offer them for free. They may point out missing duct insulation or air leaks that make the room colder than the rest.

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.