PomppeyPaul, check your license and you will notice the following.
"By the application of JAR-FCL 1.015(a)(1), the licence is entitled to exercise license privileges on aircraft registered in any Member State of the JAA".
That means, solo is "no go" in the USA.
I've this advice for you. Be aware of your liabilities as a foreign pilot before jumping into the cockpit in the USA. Make sure you moves are in compliance with the FAA and insurance requirements.
WP