Seems like 40mm isn't a very far distance. I understand that this is a PoC, but it seems like making this work from a distance is more "important" than having a low delay or super accurate precision.
They fundamentally measure the channel between arrays of neighboring electrodes. That makes them self shielding (like a Faraday shield) since they typically are designed to be relatively immune to uniform changes in coupling. From any distance comparable to the size of the touch screen the differential coupling to electrodes falls off exponentially. Near the screen they fall off 1/d then 1/d^n dominates farther out.
In order to avoid interfering with other parts of the device, they tend to be highly encoded narrowband signals and change (to known good) frequencies when they detect interference. That makes most narrow band techniques less effective. High voltage impulsive noise is most likely to have an effect, but triggering ESD detection/rejection might create a sweet spot in amplitude.
However, I wouldn't write it off completely, because if somebody else can extend its distance further then I can see it becoming a concerning attack.