Have a 240V plug on dual circuits - one 30A, one 20A

If it's truly one plug, fed from 2 differently rated breakers, that's very against code. That said, I'd use it, but I'd consider it a 20a plug and charge at 16a (80% rule for continuous loads)

To meet code the two breakers would have to be the same rating and have a bar between them such that when one trips it trips both.

 

Can you post a photo of the breaker and the plug? Something doesn't sound right. A breaker for a 240V outlet should be a dual-pole breaker which can never have two different current ratings.

 

I recommend to use the chart on this page to find out exactly what kind of outlet it is. If it is a 20A outlet, then you could build an adapter cable from the Tesla 5-20 adapter to whatever kind of outlet that is (probably a 6-20).
NEMA connector - Wikipedia, the free encyclopedia

 

Ah yes, the quad 240V breakers... unnecessarily confusing.

Downside of this is that Tesla doesn't make a 6-20 adapter. They do make a 6-15 adapter which should work in the receptacle you have (6-20 receptacles generally also support 6-15 plugs)...

Tesla Accessories and Charging Adapters Charging and Adapters

As Rocky noted, you can use the Tesla 5-20 adapter and build an adapter to make the 5-20 plug into the 6-20 (the car doesn't care about the voltage difference), but that requires some additional skill (and labeling!)

 

Can you post a picture of the plug? I agree with FlasherZ that buying Teslas 5-20 adapter and then making (or buying) an adapter from your plug (we are assuming it is a 6-20, but would be nice to check) to a 5-20 would be ideal.

 

You don't need to make it yourself, evseadapters.com offers a 5-20P to 6-20R adapter for this purpose.