A faulty concept
Here's the problem. Conceptually, you believe that your house draws a large amount of power continuously... or you haven't really thought about it and assume ??? happens in your favor. It does not.
Actually - don't take my word on this, measure it - your house draws less than 100 watts of power most of the time. There are big loads, yes -- your house has a 100A or 200A panel for a reason, and when those loads are kicking they can pull all that. But an "average" American house as deemed by the EPA and power companies draws about 1200 watts average. That's 5 amps. So that's either 1/20 or 1/40 of the panel size. So for that to be possible, the vast majority of the time your house consume greatly less than 5 amps - or like I say maybe 100 watts if even that.
And... electricity does not store. You need to use it in the same second that you generate it, or...
Energy storage it is, then.
For some reason people get really weird about batteries. I don't understand the reluctance. People wreck Teslas every day, along with Nissan Leafs, Chevy Volts etc. There are plenty of cheap large batteries available for the DIYer. They really do solve this problem nicely, and there is plenty of COTS kit to do what you're trying to do. (you're not the only one who wants that).
But who said anything about battery storage? If your house is reasonably tight, you have about a 10 kWH battery sitting right there. Check out what Technology Connectons did.
Mind you, T.C. is running the A/C at midnight to buy cheap electricity, but if you look at the pinned comment, they could just as easily rig it to run in the morning and early afternoon when solar is abundant yet peak demand hasn't arrived yet. In fact some commercial buildings are already doing this.
A/C load tends to lag solar gain by several hours due to the slow-changing thermal mass of building structure.
And then, there's the old standby of every off-gridder: the tanked water heater. That plays especially well if you have a sunrise routine, because you just put the water heater on a DPDT timer - by day, it takes dump power from your solar. By night, it takes normal utility electricity, so if the solar doesn't recharge it, grid will. The British also have "hot rocks" storage radiators, which use cheap power to make materials very hot, then during peak times release the stored heat into the room air.
However, if you're turning 1 watt of solar into 1 watt of heat, that's rather pathetic use of energy. When power is valuable, you should always be using heat pumps to get 2-8 watts of heat or cool per watt you supply.
No way around permits and inspections, though.
Unless you're on a vehicle, however, you will probably not escape the permit and inspection process. Why? Because the solar panels need to see the sky, and recent legal decisions have validated cities using aircraft and drones to look for code violations.
So if the city doesn't find out about your unpermitted solar panels, the electric company sure can, and they can simply pull your connection and refuse to connect you again until you show inspection sign-off for all work.
It helps to have a fully isolated system (and one that is DC-coupled counts as isolated: that's where the only connection between grid and your system is a DC battery charger, which by definition is non-reversible).
Your questions
Is this setup really feasible to prevent any feeding to the grid? It seems like the inverters monitoring is reactive so when my demand falls, the inverter also falls, but lagging behind the actual demand curve. Is the lag going to provide some backfeed to the grid that my power company could then see?
Absolutely not. OK, the conversation these products are having is about billing/tariffs. They're talking about minimizing your electric bill on the presumption that all the equipment you're using is already safety-rated for that use and in an approved installation.
The power company also requires the equipment be safety-rated for the use. They are very concerned with anti-backfeeding protections because a backfeeding solar system can energize downed lines that are under repair, killing linemen.
At a physical level, can anyone explain how the inverter can provide power at a higher priority than the grid? I don't understand how it seems that the inverter can supply 95% of the demand overriding the supply of the grid. Like if I connect 2 batteries in parallel to a demand, I have no control over which battery gets drained first, so how does the inverter somehow have priority?
Your intuition is correct. It doesn't. Again, this conversation is about billing and tariffs. It does not absolutely separate. Some backfeeding does happen. The system is trying to minimize how much power you sell to the power company at 2 cents a kWH only to buy power later at 30 cents a kWH. So it has no safety function at all.
If this is not a feasible approach, then I guess the alternative is basically an off-grid solution where my panels/inverter are connected to only the single branch circuit or a transfer switch which only runs the solar or the grid at a single given time, but is there any solution to this scenario where if the demand on this circuit goes over the solar capabilities that it can then draw the excess from the grid? That leads back to question 1 again.
That would require either batteries, a simple/dumb "dump load" or fairly sophisticated equipment. There's no way to blend in utility power to cover shortfalls; that's one of the reasons solar without a battery is so unworkable.
The only thing you could do is DC-couple the whole thing, where the solar feeds a DC bus and so does a rectifier coming off the utility; and that DC bus feeds the inverter. The rectifier would provide the needed one-way gating, because diodes :) And this happens automagically with a basic battery system, though the battery itself can carry peak loads.
