Readers: You do not need 60A panel headroom (or really any headroom) to charge a car. See below. OP's valid, well-informed reasons are very unusual.
Wiring options
I think conduit is a great plan. For a first time learner, I recommend EMT. Why? Because it's an "Erector Set" - everything comes apart and there's no waste, nothing is glued so everything can be reused. It's also a viable grounding path, but not to a plastic case EVSE and we need a ground wire in the pipe anyway for conduit fill reasons.
I would use the green route, not the yellow route, because I disagree with opinions that Romex doesn't need protection there. It obviously does; the wall is being used to hang tools.
I wouldn't worry about hanging a junction box behind the EVSE. Just bring conduit in top or bottom. To step down from your conduit size to the EVSE's opening, just use conduit reducing washers e.g. this. The EVSE has a plastic box; it's not carrying ground so the reducing washer is just there to keep fingers out pretty much.
I wouldn't bother getting a tubing bender. I'd just buy pre-formed 90s, and LB, LL's or LR's (conduit bodies) for making turns too sharp for two sweeps back to back. A junction box (e.g. 4x4 box) also works as a conduit body - cheaper too.
99% of my work is EMT conduit, and I don't attempt compound bends, I just use simple bends and couplers. I fit pipe up to the wall, note where they overlap, mark with a sharpie and cut there with a mini hacksaw e.g. Stanley 20-807. (takes little space in my electric toolbox). Leaves a negligible burr easily removed with the multi-tool e.g. Klein 1010, that's why multi-tools are wedge shaped. Don't use a tubing cutter, ever - it'll take all day to ream out the huge burr.
I would use the green route, and use "sweeps" to make the turn from vertical wall to horizontal. Where horizontal meets horizontal, I'd use either an LB or just a 99 cent 4x4 junction box (cheapest conduit body). Wire count and box fill aren't a consideration if there are no splices.
Conduit must be built and anchored total and complete before any wires are pulled into it. This is much easier, believe you me and it also allows you to do the work in sections. I'd build up the wall from opposite ends and let the pipes tell me where they want to meet.
#6 THHN is 65A. Both can be black. It's technically possible for two #6 THHN to fit in 1/2" conduit with a #10 ground, but that will leave literally zero room for the signal cable if you want to use the power limiting feature with the current transformers. So I would go 3/4" conduit. NEC rules don't allow the signal cable to run outside the conduit for reasons I won't get into here.
Beating 20A
I’ve studied the ‘20A is sufficient’ debate but decided 60A will be best for my use case.
That might work for you, but I really do not want readers thinking "OMG I need 60A to charge an EV, and therefore I can't get an EV". For most, yes, EVs take a lot of power, but not THAT much! So 50-60A "is expensive, and may come with more headaches than you bargained for".
Now fairly unique to your situation, OP, is your locale's waiving permits for <=20A circuits. That's a loophole most people in your town could drive a Rivian through :) Most readers won't have a locality with such a rule.
Next headache: many power companies require you to file a form/permit with them too to run a high-powered EVSE. Again not an issue for little ones.
And our next stop under "headaches" is the NEC Article 220 Load Calculation. Yes, I know you say you have that all worked out, and I'm saying this mainly for the benefit of other readers. Honestly, 95% of EVers "freestyle their own private Load Calc method" and declare victory. Nope, only your AHJ (permit issuer/inspector) can do that - some use reasonable alternative calculations, particularly for EVs. Here is Sacramento's.
Notice in any legitimate Load Cal formula, how many loads get a major "discount" for load diversity - the various loads in a home are vanishingly unlikely to be maxed out at the same time. EVs do not get that - much the opposite, they are derated by 125%. Once the rest of the Load Calc is complete, the difference between that and your service size, multiplied by 0.8, is your maximum charge rate. Hold that thought.
Anyway, if your Load Calc gives you 60A of headroom, you're all set for 48A, which is the max on current Teslas but exceeds the ability of most cars. The car's limit is trending downward because the charger is actually on the car, and costs money.
If your Load Calc does not, then you really need to get realistic about 20A LOL just kidding, we'll do 60A anyway! By cheating. Certain EVSEs provide for "current transformers" to be added to the service wires. A module in the panel communicates with the EVSE and warns it when the service is about to be overloaded. The EVSE dials down charge rate on the fly when that happens. When the coincidence of loads that causes the overload ceases, the charge speed rolls right back up. This allows us to completely ignore the Load Calculation, at the cost of paying a few hundred more for the kit. The popular domestic option is the Wallbox Pulsar Plus, whose North American version supports up to 48A. Overseas it's the Myenergi Zappi. Yes, you'll need an adapter for a Tesla but it can just live on the cord.
It's a headache, like I said, but a very doable headache. Heck you could charge at (quite close to) 48A even on a 60A service. This is probably the wave of the future, and the reason we don't recommend it universally is limited availability/choice right now.
With great power comes great responsibility. The times of greatest strain on the grid are summer days from about 2 PM to midnight (A/C load is offset from solar generation because the structure of the building stores heat). This creates a "duck curve" which makes it particularly damaging to charge EVs from about 5PM to 11 PM. So don't.
Anyway, 10 years from now, the charger on the car will be shrinking as data shows it's rarely used productively. I expect AC level 2 charging will be limited to 24A on most cars. Luxury-minded people will get a "Home DC fast charger" with NO upper limit to charge rate (thanks to those current transformers). A 200A service could charge at 40kW (~160A) minus house loads.
