How can I update a stack parameter which was set by an SSM parameter?

I have an SSM parameter value set with a value I want to use in a CFN template. In the CFN template I have a parameter configured as follows:

Parameters:
  DDAPIKEY:
    Type: String
    Default: '{{resolve:ssm:DDAPIKEY:1}}' 

I then use this parameter as an environment variable in a lambda function. This works for the first deployment just fine, but if I change the SSM parameter value and redeploy the stack my expectation is that my lambda function would be updated. But given how CFN default parameters work (they only set the value the first time) I'm out of luck. Subsequent deployments do not update the environment variable even if the SSM parameter value is changed.

Am I mistaken about something or are there ways to work around this?