Have to read the documentation very carefully.
https://video2.skills-academy.com/en-us/powershell/module/az.resources/new-azresourcegroupdeployment?view=azps-4.6.1
-TemplateParameterFile says:
To use the dynamic parameters, type a minus sign (-) to indicate a parameter name and then use the Tab key to cycle through the available parameters.
-TemplateParameterURI doesn't say that so it doesn't seem like it is supported.
I've moved on to -TemplateParamaterObject and adding my values there. Which will create a new set of questions.
(they really need a more general tag for new-azresourcegroupdeployment)