If you're going with one of the latest high efficiency inverter systems, you probably won't need a gas backup (in Seattle). They can extract heat down to almost zero degrees. And for those rare days it gets below freezing (in Seattle) electric backup heat strips would cost less over the life of the equipment (figuring in up front and ongoing costs).

Any of those systems should be fine if installed properly. And stay away from Nest thermostats with them.

System will be heat pump/gas furnace combo.

This is also called a dual fuel system. It is more expensive than a gas furnace and AC only system. The primary advantage of a dual fuel system is being able to switch to furnace or heat pump heating depending on the cost of gas or electricity. If you post the gas and electric rates a calculation can be done to determine which fuel is cheaper with today's prices.

Seattle has mild winters and summers. I am not sure if you really need to spend the money on a dual fuel fully variable or modulating HVAC system. The list you provided is very nice but they are going to be expensive.

How much heat and how much flexibility you need depends on many things, but I trust an honest load calc will be prepared. How well insulated your old house is or isn't how tight it is or isn't., etc.

I'd thought the Greenspeed-type heat pumps were for places where frequent sub-freezing temps were common. I suspect your money will be better spent with a more conventional, less expensive heat pump (performance wise) and a gas furnace for a boost. The gas furnace can also help recovery from overnight setbacks if that's something you prefer, as many do. A heat pump can struggle to recover from more than a few degrees of setback.

I'm a fellow homeowner though I've bought two completely new systems for my two homes in the last 4 years. You're looking at top brands, that was something I preferred too. Recognize they have different lines (and different tags) that can affect price and, to a lesser extent, features. I wound up getting Bryant equipment in both places - the same as Carrier, same models, slightly lower cost. In the old days, like GM making Cadillac vs Chevrolet.

Beyond that, the good advice I got was that the name on the workers shirts means more than the names on the equipment. Meaning - choose the contractor by reputation and recommendations and pay less attention to the equipment they provide. You're buying a service as much as hardware and a top contractor can make a system out of lower quality equipment perform well, where a lower quality contractor can take top equipment and make a mess of it.

Good luck.

I concur with Elmer that whomever you select to do the installation is important to achieving the full potential benefit of whatever system you choose.

I recommend an objective look at your home's thermal envelope--insulation, windows, air sealing etc. before choosing an HVAC system. And don't forget the "V" in HVAC: your HVAC designer should also consider your home's ventilation needs.

1. Does anyone have experience with any of these systems, or know of any reason to go with one brand over another (specifically with respect to this type of system).

Of these major brands you list, some may limit the variable nature of which these systems are capable of. Not sure if they still do this or not, but the Carrier models of the recent past limited their models to 5 speeds. Things change with time, so these models may no longer be made.

The other is proprietary controls. Some you can use older controls at a cost to performance as in most cases using older controls will turn the machine into a two speed machine.

None of these brands AFAIK or can prove make the parts "namely the compressor" -- that drive these units. Nearly every part that makes the machine run are made in other countries and at best are merely "assembled" in the US.

If the pandemic has taught me anything... assembled in the USA is NOT the same thing as "made in the USA". Whether you buy a fully variable speed AC (Inverter) or not, these things are the same for lesser models.

2. In particular, does anyone have experience with the proprietary thermostats that you use with each? This is my biggest reservation. You need to use the communicating thermostat that goes with the system, and I am concerned about that kind of proprietary tech from a company that isn't in that business. There are all sorts of reviews that the thermostats are incredibly buggy, updating constantly, and the tech is clunky.

Why nearly all major brands chose to take this approach to control their upper end variable (inverter) systems I believe is partly to cut out the nests, and ecobees of the world. But with that comes trouble. Namely expense and as you suggest buggy kinds of problems.

There is another brand of Inverter that doesn't do it this way. All you need is a simple 24 volt signal and the "smarts" is in the outdoor condenser. (Bosch)

Another brand that has gotten away from proprietary thermostats is Amana. However the Amana will require the Amana furnace paired for their inverter as the furnace contains the communicating functions to communicate with the outdoor inverter.

Communicating is buggy for similar problems that make your internet connection go down. Because they use thermostat wire connecting parts and pieces of the system to the "network" that runs or tells the AC system "what to do".

So any connection problem or interference can cause intermittent "communication problems". The Bosch Inverter solves those problems completely. As it's doesn't rely on communicating the way the big box boys chose to do it.

The problem? Bosch is a disruption type technology. There is risk when competing with goliaths in the industry, for fear they squash you like a bug. The manufacturer or "owner if you will" of Bosch tech, doesn't make the unit they designed. They went out hired a manufacturer to make it so it's German engineered and made in China.

Currently Bosch are back ordered here and have been for months... but you may find the same thing when dealing with major names as many of these parts made to make these systems come from place like China and elsewhere.

3. There seems to be a lot of advice that the installation/installer matters more than the system in many ways.

Installation matters. In the realm of variable speed AC systems / heat pumps (Inverter driven) -- This equipment is expensive, requires a good amount of knowledge above that of installing a traditional single or two speed machine.

In the communicating realm of machines one must also know what causes networks to go down and be able to fix those problems in addition to everything else we must know. Some HVAC companies that don't get into these Inverter driven or "proprietary controlled" things are more likely to try and talk you out of it. They are also dangerous --- touch the wrong thing the right way and you could become a krispy creme.

While one could argue a simple single speed system is also dangerous.

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I chose the Bosch Inverter for my own home in Katy, Texas in October of 2019. I don't regret that choice yet.

Reasons: cut my electric bill in half. Does a much better job dehumidifying.

In a more mild climate like Seattle... I believe this choice has more to do with electricity costs and better over all comfort. Many parts on the west coast pay a higher utility rate so these machines can pay for themselves over time and use.

If you'd like an objective view rather than an endorsement of one brand over another, here's a link:

https://www.pickhvac.com/central-air-conditioner/trane-vs-carrier-vs-lennox-review/