After some research it appears my cigarette lighter is 20 amps.
Yes, it may be fused at 20 amps.
The cigarette lighter plug, the part that you'd push in, may also be rated at 20 amps. Problem is they are a poor spring contact and as they work loose, the connections get flakey, resistance goes up, voltage drops, all kinds of issues.
Also, like I said before, tapping into existing vehicle wiring is a good way to introduce noise into your radio.
It's your radio and your vehicle, do what ever you like. If you are asking for advice, don't do it as a long term solution. You'll just end up back here asking for advice on why there's so much interference on your radio, why the power is intermittent, etc.
There is a very good reason we are telling you to connect the power directly to the battery.