Thank you for posting.
It seems you have performed all of the necessary prerequisite steps and even had the web sharing functioning.
What happens if you perform a basic port scan? For example, using telnet in the Command Prompt from a remote location:
telnet ServerDNSName_or_IP 5003
When you set up the favorite host in FileMaker Pro client, is there any difference when you use the external IP address versus the DNS name? This will determine if the issue is with the no-ip service.
Since you can connect locally, it indicates that the host and client machines are set up properly. I agree with your assessment that the issue is likely to be the router configuration or the Dynamic DNS service.
It sounds like you have done the correct steps.
The only gotcha that is sometimes a problem, in some routers you need to click an apply button for the changes to be made.
Have you viewed the router settings to verify the change? (both TCP and UDP are set?)
This is a step by step that is illustrated.
FileMaker - How to Setup a Network Router for FileMaker Remote Access