The big difference between the new use of Tol- and the new verb Nîdha- is that Tol- is written by Tolkien to be an auxiliary verb, whereas Nîdha- isn't, it's just another new way of expressing future intent. Here's some of the notes. (Bits in [brackets] are my explanations).
"In T. [Telerin] and S. [Sindarin] NID became used exclusively of 'rational' purpose and will. S nîd meant 'full vigorous purpose or the exertion of will'... and from it a weak verb nîdha was formed [this means it takes the normal past tense endings, Nîdhant = he was determined etc.] and applied to exertions of strong will in major purposes (am determined to)."
"The older verb Nîdhin ... was weaker, and sometimes became no stronger than 'will' in E. [Eldarin, i.e. the original Elvish before Quenya and Sindarin] ... I will do it, I mean to do it, & so could operate sometimes almost as a future auxiliary: Nîdhin mened, I have a mind to go, I intend to go."
This is very specifically written as 'this is what it used to be', not 'this is how it is now' but unfortunately Tolkien didn't give us any actual examples in modern Quenya or Sindarin...
However! Having thought about it overnight, and my brain poking me with the King's Letter, I will go and edit that lesson to use the gerund instead of the imperative as that seems to fit better with other modern Sindarin. It was a toss up either way really, but I have now changed my mind