Ah yes! This explains the behavior. It is almost certainly being tripped by the GFCI function of the breaker (rather than the thermal or magnetic trip components which are for overload and short circuit conditions respectively). We have seen Tesla's (generally with the UMC - interesting that your OpenEVSE is also experiencing this when it did not with other EV's) causing nuisance trips like this. I think though generally replacing the GFCI unit (in this case the breaker) with a new modern one has resolved the issue for most folks.
Question: Where is the receptacle? Is it outside in a potentially wet location, or is it inside in the garage in a dry location?
From a 2017 NEC code standpoint in article 625 it says receptacles for EV have to be GFCI regardless, though it kind of chaps me since the EVSE also has GFCI built in. I personally think it is not unreasonable to have a non-GFCI receptacle for EV's as long as it is in a dry location. The EVSE plugged into that receptacle will have its own GFCI function within a 12" distance from the receptacle. I might be tempted to swap that breaker with a non GFCI one if it was in a fully dry location, however, I can't recommend that as it is against code and you most certainly would not want to do that if it was tripping due to an actual real ground fault. You would just be bypassing that safety feature which was working.
Since we have identified that the issue is likely GFCI related and that something is already wrong with your existing EVSE, I would definitely try it with the Tesla UMC with the right adapter (though it will take a few day to get that probably).
I hate how expensive GFCI breakers are. $112 seems unreasonable. This is why the State of Oregon has whacked nearly all the new GFCI requirements in 2017 NEC. They accidentally missed the one that snuck into article 625 for EV charging ports. The committee did not get a chance to review that one since it was a last minute emergency change to insert it to the 2017 code.