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Far too many variables to say, but the HPWC connected to those same wires(presuming they are sized for a 6-20 load) will get you no more charging speed at all. That 6-20 should get you around 16 mi/hr of charge rate, which should be plenty for most users. Don't forget the 30% tax credit for new charging equipment/install.
I imagine an electrician would do such an install(direct replacement) for $200 or less. OTOH, if that's currently in a garage the electrician is likely to want to replace the wiring with conduit-based wiring(or MAYBE run that current wiring through conduit below 7') since NMB isn't supposed to be accessible(I think the rule is 'below 7 feet above the floor its gotta be in a wall', but don't quote me on that).
6-20 is a great, cheap option especially if you already have one available! 16 mph is generally plenty for most people.
However, it may be worthwhile to swap the outlet out for a new, industrial grade one like the Hubbell part #HBL5461. Tesla recommends a high quality industrial grade outlet. Lots of color choices if you don't like the brown one in the link below also.
Order Hubbell Receptacle, 20 A Amps, 250V AC, Flush Mount, Single Outlet, 6-20R, Brown, HBL5461 at Zoro.com. Great prices & free shipping on orders over $50 when you sign in or sign up for an account.
6-20 is a great, cheap option especially if you already have one available! 16 mph is generally plenty for most people.
However, it may be worthwhile to swap the outlet out for a new, industrial grade one like the Hubbell part #HBL5461. Tesla recommends a high quality industrial grade outlet. Lots of color choices if you don't like the brown one in the link below also.
Order Hubbell Receptacle, 20 A Amps, 250V AC, Flush Mount, Single Outlet, 6-20R, Brown, HBL5461 at Zoro.com. Great prices & free shipping on orders over $50 when you sign in or sign up for an account.