Hi Eli,
Let’s check first a model method to get a model which can be easily updated, and then look into Surface Deformer. (To use a Cube means to set the UV data for your purposes!)
I have—however—recreated your set up, so far possible with the given data. I created a honey comb object, and used it to create an Edge-to-Spline object. I had no trouble doing deforming it with the Surface Deformer. Which allowed me to test what could be the reason for the problem. What doesn’t work at all, is, when the caps are “on”. Was that not shut off perhaps in your model.
A scene file would be helpful. Here is mine, and the connections are not perfect, hence—why I will show you a different route.
https://www.amazon.com/clouddrive/share/zTwHMJ4aUS8E6J1UlC3it48xvBCf9ENj4N5rxlnIUQ4?ref_=cd_share_link_copy_flash
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I had to do this for friend, many years back, for a Silicon Graphics computer ad-animation, nearly a decade ago.
Perhaps a little bit too long, but to get this honey-comb pattern is described here:
http://www.cineversity.com/vidplaytut/mograph_hexa_honeycomp
It is an older clip.
A series that might help:
http://www.cineversity.com/vidplaytut/industrial_modeling_-_holes_part_01
Part five and later perhaps especially
Based on creating with two “Plane” objects the hexa pattern base, as discussed in the tutorial, you just can use (see attachment. disc.1 or disc.3 [scaled]) a shape like this, to create a structure as needed. This allows an easy replacement of the core file, even a dummy/proxy is possible.
This allows you to have a nice and clean low-res mesh. Which would be impossible to bend. Where you need to bend it extremely, you can cut [Knife: Line/all options unchecked:visible, n-gons, etc.]
With tis established, the front needs perhaps some cuts as well. But less than the rounded sides. Being straight cuts allows the Phong tag to do the work. See file 02.
I have worked from top to bottom [Object Manager], I hope that guides your exploration. My file is sketch - use a cut-guide - or constrain the Knife [shift key]
Let me know if there is a question. Perhaps try to have the cuts in the single object already, with symmetry in mind, so points connect to points!
All the best