Jef,
Several recommendations.
1.) Use tables for dynamic information (like parameters read from the model.) They are designed for this and will automatically populate when different formats are applied to the same drawing or a new drawing is created from a template.
2.) Use symbols for static information that will never change. Borders, zones, logos, etc.
3.) Use the built in drawing system parameter &model_name in a table to display the name of the model. (There is no need to create this in the model relations.) Also, this parameter will never point to the drawing, even if no model is present.
4.) To reference parameters from the model, but not have the drawing replace them with "dead text" if they're missing or use the drawing's value instead, create single cell repeat regions that only display that one value. Set the repeat region parameter to &mdl.param.value and the repeat region filter to &mdl.param.name == <PARAMETER_NAME>. Since there will only be one parameter in that one model with that name, the repeat region will never grow. This is a very robust way to reference model parameters.
Finally, here is a link to the most recent System Parameters for Drawings