Installing Conduit/Wires for Tesla Home Charger

I just recently bought a house, in Washington State, Shelton, and am looking to hook up my tesla wall charger. Currently just charging with a normal outlet, only getting the 4 miles per hour. The house is weird in that the circuit breaker is inside the office, quite a bit away from the garage. I had an electrician come out for a quote.

Their suggestion was that we could install the charger outside, we would just need to go up and through the attic to the other side of the house. As the main breaker box outside is on the opposite side of where the charger would be installed. Initial quote was $3k.

I am wondering if I could save, if they would even allow me, to install/run the wire and conduit myself. Having them just hook up the wires to the electric box.

There are quite a few regulations/rules I know to follow by. The charger needs 2x 6AWG THWN2 wires for the power. Then a 10AWG for the ground, totaling 3 wires.

NEC regulations for #6 is max 4 for a 3/4 conduit. So, I should be fine with 3/4 for 3 wires.

I am also aware that all conduit must be strapped within 3 ft of any termination or boxes. I am thinking of stainless steel or some sort of strapping that would be rust/weather proof.

Would I be able to run the wire and conduit myself, or would most electricians not do the work since they didn't run it themselves?

I know the most expensive part is going to be the wiring, as I need around 150 ft, and #6 costs around 0.92/ft and #10 around 0.32/ft.

If there is anything else I may need to know, suggestions, tips etc that would be greatly appreciated.