FireRob,
What most of us do is to buy the standard flat blade adapters for the other two standard RV plugs and use our rigs OEM cord. In your case you can get a 50 to 30 adapter for about $20 and you already have the 30 to 20 adapter. And you'll need the 50/30 adapter anyway for CGs with 30A only.
You may/may not be able to run your AC. A 12A AC might be OK while a 15A AC is less likely to be OK. Monitoring the voltage and checking the adapters for excessive heat can help determine if it's OK.
Be aware that the standard household plug is usually one of many 15A rated plugs on a 20A CB so there might be other draws and long wiring to consider. Considering you're in hot Fort Worth you might want to consider installing a 50A plug in the house.
I have a 25 ft 50A extension cord plus the rig cord that I use. Sometimes extension cords are far cheaper than installing a closer plug and can be used in other locations.
