So, basically,

1) when looking for a nested name, do normal lookup
2) if that didn't find anything, look into the template parameters

If I then _don't_ want to expose such a template parameter name, what do I do?

Looks like you have not read my proposal :)
Here is an excerpt from it:

What if I did not want to redefine them?
First of all, it turns out that they are a crucial part of an interface and often or always are of interest to end-users. A quick survey of STL shows that all containers declare all their template parameters and make them available to users.
Secondly, if there will be found a compelling enough argument for having the possibility to disable the feature, an approach similar to “= delete” can be adopted.
(or you can declare them in private section, as an alternative)

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