BS”D
DY: Thanks for the Maare Mekomos. I could not find the Chazon Ish inside, could you please give more detail. As for the Tzitz Eliezer, he seems to be saying (his second reason which we are dealing with) that the “Uvda D’chol” is that his body isn’t resting. Obviously that is not a Klal (or running L’dvar mitzva or using a wheelchair would also be Uvda D’chol), so that itself needs to be analyzed. Furthermore, he seems to settle on a general idea of “Zilzul Shabbos” (last paragraph), which I agree would apply to cellphones (“Libi Nirah Li”), but that would be no different than those who already play basketball on shabbos inside an eruv.
Additionally, if you look in Chelek Alef where he first brings the Chasam Sofer & Ramban, it is specifically because one can not do “Shabbosdik” things on a train (which is the chiddush of the CS).
In short, if you do go with this Tzitz Eliezer, he equates Shevisah with Uvda D’chol (questionable), of which the reasons (of Na V’Nad) would not apply to cellphones. If your argument is that it isn’t “Shabbosdik” and therefore Uvda D’chol, that horse has left the barn quite a while back.