Unfortunately, you can’t work your full-time American job and get a visa in Germany. It’s a non-starter.

There is a special visa if you want to join a Sprachschule to learn German. But they won’t give it to you unless you’re in class 4 hours a day.

The last option is asking your company to put you on a German payroll service which effectively acts as your German employr (pays taxes, health contributions, etc.) This can be a few thousand $$ a year though.

I looked into ADP when I was researching my options but a quick Google search will turn up many more.