You can have your cake and eat it, too. Re-purpose the line for 240v 20a and put in a 6-20. Use the Tesla 5-20 adapter on your UMC and make yourself a 5-20r to 6-20p adapter. This will give you 240v 16a charging for 3.8kW. Be sure to follow code for the work which usually includes marking each end of the white wire with red so that it's clear that it's now a hot.
If you don't like using an adapter this way, you can purchase a J1772 EVSE like the
16A Level 2 EVSE LCS-20 | ClipperCreek (which is designed for a 20a 240v circuit) or a JuiceBox which can be configured for one. Neither one comes with a 6-20 plug, so you'll either have to put one on it, or hard wire the unit...or you can get an HPWC and configure it for a 20a circuit and consider yourself future proofed.