opened your file, cristal clear and well organized, but there’s one thing…
you have more text tags (A) than points (B) 
by using Closest Point on the Text Tags, for each Text Tag it will find its closest Point (C) regardless if that point was already the closest of another Text Tag
so you know in advance that at least the amount of points (A-B) will result in duplicate instances (I say duplicate, but it does not necessarily mean they are 2… they are for sure 2+ but can be many)
if you want to know which ones are the points which are collecting multiple tags, you can do something like this, where:
height from text 4_inno.gh (82.8 KB)
RED marks = original points which are not Closest to any Text Tag, so they were not moved at all
GREENISH marks = original points which are the Closest Point of 2+ different Text Tags simultaneously (so will originate duplicates with same X, Y coordinates and different Z)
you’ll notice that over the head of each greenish point there are indeed 2+ different resulting moved points, for instance:
sometimes they are even impossible to notice because they share the same Z coordinate, but still they are double entities:
I don’t know it this was your original intent, but this is what comes up by using Closest Point 
[edit] let me say first that I have no idea whatsoever what those points/heights represent in real life, but my head tells me that an alternative approach -which might easily be completely wrong- would be to compute the Voronoi (oh yes) diagram of the Text Tags, in such a way to identify for each Tag a sort of “area of influence” in the shape of its cell, and them I would push-up each original_Point that exists inside of each cell by the respective Cell_text_tag value
this is the Voronoi diagram of the Text Tags (after correcting a single text tag that did show “210” value, and because everything else was in the range 0.64 to 16.57 I thought it had to be 2.10 instead) green are lower values, red are higher ones
and this is how it looks after pushing up the Points depending on which cell they belong to (file is pretty calculation heavy, I guess around 20 seconds…)
reuploading also the Rhino file because it had many duplicates both in points and text tags
height from text 4_inno_Re.gh (71.9 KB)
larger dataset_without_duplicates.3dm (3.1 MB)
another approach (and I guess the best one) might be to mesh-triangulate the text tag points, then project your original Points onto that mesh in such a way to take into account linear height transitions… the way I presented the above Voronoi thing was more a “stair-step” approach, like if the whole cells were planar stair-steps and Points were just projected into those
(wow, actually doing that might save very much processing time lol)
(no it doesn’t
)
here are the points projected on the Delaunay mesh created from the Text Tags, just for reference
height from text 4_inno_Re_Re.gh (67.3 KB)
