Hi there, and welcome to the forums! Although we have listed on the なさる grammar page that it can be paired with the stem form of う and る verbs, in reality this is actually extremely rare. なさる is almost exclusively used either by itself, or when paired with する verbs.
I will add a note to the なさる grammar description about this. になる on the other hand will often pair with either the stem form of う and る verbs, or する verbs.
The explanation suggestions that いらっしゃる is used for いる, くる, or いくand also the て form of these verbs but then the examples go on to show it is often used for the て form of many other verbs too eg. 田中さんは今本を読んでいらっしゃる
I think this needs to be made clearer as it is very difficult to know when to use いらっしゃる vs お~になる when those questions come up.
In the explanation where it says that this verb can replace いる, くる, and いく, that remains true for the て form of other verbs, as the いる (one of the verbs it can replace) in ている is what it is actually replacing.
It is also specifically mentioned here in the explanation - いらっしゃる may also be used to replace いる, くる, or いく when they are attached to the て-form of another verb.
Hope this helps!