I am amazed. All the electrical experts giving advice and opinions to the OP and not one of them has addressed the original question :
have 2 separate 110v circuits close to the compressor.
Can I use the hot leg from each of these circuits to supply 220v?
The answer is maybe. IF each "hot" leg is from the same side the incoming line then NO.
If each "hot leg" were to be from opposing sides of the incoming line then YES.
Is this legal? I don't think so.
Is it safe, I have no idea.
Would I do it, NO.
What you did may or may not meet your local code- call and ask if you want the correct answer.
You are correct in your thinking about the 30 amp breaker with a 20 amp load. No different than a 15 amp breaker and a 3 amp load in a household circuit throughout your house.
The circuit breaker protects the wire in circuit NOT the appliance at the other end of the wire.
As long as the wire size is correct for the breaker rating you are fine. Can the wire be larger than the breaker rating, certainly.
IMHO, and it is only my opinion, if I had your wiring setup in my house, I would sleep fine.
Is your insurance valid, I have no idea, ask your agent.
I believe you could modify your setup and pass an inspection. You would need to route the incoming power line into a properly sized manual dpdt break before make switch with one side feeding the dryer recepticle, the other side feeding the cable to the aux. outlet. But that again is only my opinion, ask your inspector.
I am not an electrician and I did not stay at a Holiday Inn Express last nite.