Thing about a trencher is it's real easy to hit other utility lines and suddenly you know why they wanted $25/ft. One way to work around that is use Rigid conduit. This only needs to be 6" below surface (top of pipe 6" below surface) where vehicles do not drive over. Expensive pipe, but easy/safe to trench.
6Cu/4Al for a 20A circuit. Seriously?
A little bit of voltage drop never hurt anything, as long as it stays little. Realistically you won't run 20A on a 20A circuit, the legal maximum for continuous use is 16A. Let's look at these.
First what if you just used 12AWG? At 5A (actual draw), your drop is 1.96%. At 10A actual, your drop is 3.91% which is absolutely fine and won't hurt a thing. At 16A, 6.26% - you might see an incandescent dim very slightly when you turn a 1500W heater on, but again, not a big deal. You have worse with a power tool on an ordinary 16AWG extension cord.
If we bump to 10AWG -- 5A 1.19% -- 10A 2.37% -- 16A: 3.78% That seems like plenty to me. I'm not even going to look at 8AWG. You get the idea: these wire upgrades are pretty optional.
But if you're so worried about voltage drop that you'd spend almost $2/foot for wire, let's look at it another way.
Transformers!
I routinely see 5kVA (5000 watt) 240-480/120-240 transformers on Craigslist for about $100. Bring 240V from the house. When voltage doubles, voltage drop quarters, so this works very efficiently. Feed the transformer primary (jumpered for 240V). Jumper the secondary for 120V and feed a tiny "main" 120V panel. If we aim to draw 16A@120V, that's only 8A@240V. Voltage drop calc says: 2.42% drop with 14AWG wire. 1.57% drop with 12AWG. Very acceptable!
Suppose we later decide we want alot more, and want to "max" that 5 KVA transformer. Fine, just push the 12AWG to its 20A limit, and have 3.91% voltage drop, again quite livable.
So the transformer plan is one you can keep in your back pocket in case the voltage drop on your 12AWG wire starts to annoy, or you just want more power. Simply install a subpanel, maybe a 6-8 circuit type (2 for building shutoff, 1 for your primary load) and wire it so it could either be a subpanel or a main panel. Once it's more than a simple circuit, you will need a grounding rod system at the garage.
Speaking of $2/foot, stop buying at Home Depot. Period. Done. Home Depot is cheap on the things they know you'll price-check them on, like rolls of #14 Romex. But by and large, they charge you "gotcha" pricing, because they know you have no idea where to find building supplies otherwise. HD's "by the foot" price is simply outrageous. They want $5 for 120mm square boxes I pay $2 for. Five for $2 for couplers I pay 16 cents apiece for. It's completely insane. Their selection is also terrible and they don't stock key parts of wiring systems like surface conduit. Find a locally owned proper electrical supply house, or several, and cross-price them on the wire and parts you need. Get a shop whose prices you like and get loyal to them.
Best Answer
There is more to it that you may not realize. By using manual switching, you inherently prevent even the remotest possibility of back-feeding the utility grid with your solar power. It is not physically capable of being connected to both systems simultaneously. As soon as you "automate" this, you introduce the possibility that something could fail in an unsafe state. The result could then be that your solar system is feeding the grid and a utility line worker is killed by it because he is working on the wires when your "transfer switch" screws up and connects. For that very reason, as soon as you go with anything other than a manual changeover switch, it must have certification that your power utility accepts regarding its safety.
You will need to start there before you buy anything.
And to answer your question about using solid state switching, absolutely not. Solid state switches "leak" when they are supposedly off. The leakage is minimal and for general purposes is often ignored, but for something like this it is potentially lethal.