Since you already have a 50A circuit for charging your upcoming AWD LR Model 3, a Corded Mobile Connector wouldn't require any additional electrical work if you want to go from about 32mrph to 37mrph on that 50A circuit with a NEMA 14-50 outlet to use. But think you weren't sure if your ChargePoint was plugged into one or if it was hardwired, so that would be something to figure out. If hardwired in, I don't think it would be a big deal (time and $s) at all to remove it and connect the existing wiring to a new outlet since the wiring is already run.
If you want to charge even faster at apx 44mrph with a HPWC, you'd need to at least upgrade your wiring and circuit breaker to 60A which you said you know.
Does your daily driving nearly deplete your range in your car every day or are you just going to be topping off to your desired range every night or when you want and need to?